I was considering adding to this topic:
Single stage V-1710: options for improvements?
but this thread's been active a lot more recently and covers most of the same thing (and a lot more).
Addressing that specific topic of single-stage first:
The 7 notable mechanical limitations/problems the early (C series -mostly commonly the V-1710-33 of the P-40B/C/Tomohawk -Curtiss Model 81) were:
1. relatively weak reduction gearing making any stress of overboosting beyond the relatively modest performance limits very destructive to this engine (I believe this is what gained reputations for stripping gears with the AVG's rather abusive use of the engine, possibly some cases in the MTO as well) This was addressed with the E/F and later series engines to the point of often tolerating very heavy out-of-spec abuse. (this might have still been a bottleneck for overrev, but the prop/hub/blade-mounts would likely be a bigger bottleneck)
2. crankshaft strength and to some extent overall finish (I've been digging around for the disucssion that had more specifics on this -particularly the actual changes between the C and E/F series and later models of the E and F prior to the added changes with the G series, but I haven't found it yet). From what I recall, the F series received a smoother finnish than the C series and had strengthening allowing higher power levels. (the well-balanced design of the C series already made for smooth running and ability to overrev -unlike the Merlin and some others- and made such more tempting for pilots to exploit, or attempt to)
3. inability to use the smaller 14-tooth supercharger gear needed for 9.6:1 supercharger operation (8.8 uses a 15-tooth gear) due to structural limits of the existing gear pitch/width requiring a redesign of the mount to allow space for a thicker gear. The required changes would have disrupted production and added costs the Army was unwilling to pay. (this was the main reason for delay in adopting this iirc, there's been more accurate and detailed discussion on it before, and I might have the exact terminology wrong, but I think this is about right)
4. Lack of 2-speed drive. Similar to the gear-tooth issue but requiring even more dramatic redesign of the compact accessory section of the engine, presumably with greater overhead in production changes than most other design problems/fixes. (and wouldn't benefit turbocharged engines) The Army would likely sooner fund an auxiliary supercharger than 2-speed drive given the concerns over efficiency of production.
6. Backfire screens adding drag in the engine manifold and reducing manifold pressure and/or mass flow for any given altitude and supercharger configuration. These were later removed as unnecessary some time after the 9.6:1 supercharger had been introduced. (I think the P-39M is the only fighter to receive a 9.6:1 supercharged engine retaining those screens)
7. Kink/bottleneck in the supercharger intake manifold around the carburetor/throttle body. This was one issue that I don't believe was ever solved and was also mainly limited by the Army's unwillingness to invest in the necessary changes to production. (this problem was noted pre-war, perhaps even prior to any large scale serial production had started but possibly after initial production tooling had been laid out -I'm not sure, but that seems likely given the cost/delay for modifying a non-production design would be so much less as to make that ridiculous, even with a turbocharger-oriented altitude performance program)
The latter issue is rather similar to what the pre-XX series Merlin suffered (in terms of intake chocking the supercharger -noted by Hooker when he began work on improving it) with the exception that Allison's engineers and the USAAF were aware of the problem when RR seemed less so until Hooker inspected the design. So it seems they had the engineering ability to solve (or at least start work on improving) the issue but the Army declined to fund such changes. Solving that issue (like with the Merlin) should have reduced charge heating and increased critical altitude for any given manifold pressure, resulting in higher power levels at any given pressure and higher maximum pressures without suffering detonation. (the latter more important with 9.6 superchargers and possibly Pre-J P-38 given the poor intercooling and any little bit of reduced charge heating in the supercharger still being relevant ... though clearing that kink should make ALL turbo installations less bottlenecked and more efficient)
Lack of aggressive/exhaustive testing combined with relatively conservative ratings in general seemed to plague the V-1710 as far as WEP and take-off ratings went, possibly even maximum continuous power. The E and F series should have been capable of pushing well beyond 3000 (perhaps even 3300-3400) RPM and unauthorized operation at such speeds were noted (let alone post-war tractor pulls and such pushing them far far higher -even without the G-series crankshaft) but no official testing leading to up-rating seems to have been done on this. (reduction gear and prop would be the breaking points for overrev, but without proper testing of those limits, there'd be no reference for even designing around WEP limits and no context for aircraft designers to appropriately test their aircraft and propeller combinations -or note whether different reduction ratios would be needed) The smooth running nature of the engine might have made a 3000 RPM max continuous rating also possible, but specific limits on boost pressure at that rating would also have to be noted separately from military/WEP (or 30-minute limits).
Likewise, tests specific to 100/130 and 100/150 octane fuel should have been completed sooner (or used more incomplete results for operational clearance/expanded operational testing).
It seems the British Air Ministry and Rolls Royce were both more aggressive with testing WEP and general engine limits and more willing to push less than exhaustively tested ratings before putting them into practice. (given the more conservative and stringent nature of Aircraft design specifications the USAAC/AAF and USN had already established pre-war, this seems less surprising, and the V-1650-1 somewhat reflects this as well given the apparent lack of WEP clearance compared to the contemporary Merlin XX and 45 series)
Overrev is particularly significant as it would have boosted critical altitude as well, and partially side-stepped the 9.6:1 gear delay. (exceeding 3200 RPM with 9.6:1 gearing would also seem unwise as the impeller tip speed would exceed the speed of sound by a significant margin even taking generous charge-heating into account, and would also exceed any real-world tip-speed examples during war-time use, while 3200~3250 RPM itself would rather closely match the tip speeds employed with the V-1650-1's supercharger in high gear, or the experimental 10.25" diameter 2-speed single stage Allison supercharger at 9.6:1) On that note, an 8.8 supercharger on an engine running at 3300 RPM will result in a speed equivalent to 9.68:1 at 3000 RPM. (so very similar tip-speeds to 9.6:1 engines at normal military power operation)
Overly conservative ratings can be more dangerous in practice due to leaving the real, hard, extreme operating limits of the machines totally vague and questionable, resulting in a rather high incentive for individual experimentation and unauthorized operation in the field with no reference to how dangerous such operation was. (compared to pushing the Merlin beyond WEP specifications, which was much more reliably going to end in failure) The rather dramatic warning of 57" boost limit on the 9.6:1 engines seems to be among the exceptions of extreme limits being posted, but even that is exaggerated in its imperative as experienced showed pushing closer to 60" was still possible without detonation on those engines, and their notice doesn't note this behavior at all. (P-39N flight testing even lists use of 59.8" manifold pressure being used)
OTOH, there may have been cases of Allison recommending/clearing use of certain engine settings, but the USAAF never implementing them. (2000 HP with 75" MAP on 100/150 fuel was cleared for the P-38L's engines, but may not have been officially cleared for P-38 operations ... though obviously would at least have given a nicer guide for unauthorized use operationally)
150 Grade Fuel
Making improvements on the base, single-stage engine is pretty universally important as it extends usefulness to all existing designs using the engine (no serious modifications to address changes in weight or changes in overall dimensions) while equally extending those improvements to engines using turbochargers or external auxiliary superchargers.
Now, to the points beyond the basic single-stage engine:
The big overarching issue here is the Army simply should have supported Allison's R&D far, far better, and put those hyper-engine projects at much lower priority. This includes putting turbocharger+intercooler development on higher priority too, specifically for technology making it more suitable in small, sleek single-engine aircraft.
Turbos have 2 big issues for small fighters (P-39 is a great example in the extreme here), their own size/bulk, and the size/bulk/drag caused by the intercooler. The larger the turbo, the larger the intercooler and resulting ducting, and restricting turbocharger design to relatively large units precludes the possibility of medium-altitude optimized variants with reduced size/weight/intercooling capacity requirements. (say targeting a critical altitude in the 20,000-25,000 ft range) Or even having turbos small enough to allow reasonable use with no intercooling at all, more akin to Allison's non-intercooled auxiliary superchargers.
This issue can be drastically reduced by adopting a liquid intercooler, and Allison could (with enough funding) have tackled this engineering project themselves, optimizing around GE's turbochargers. (this would have been a critical development all around, and really the biggest single achievement for extending the V-1710 beyond single-stage operation) Given the coolant loop would be shared with the engine's own cooling system, this seems a reasonable thing for Allison to invest in developing rather than GE. (and turbocharger relevant, thus more likely to gain Army support/acceptance) If this work had been done early enough, the P-38 could have abandoned its wing intercoolers sooner and gained both power and (potentially) leading-edge fuel tanks in the wings for longer range operations. (granted, still needed cockpit heating, dive flaps and hydraulic -or tab- boosted ailerons to make a really potent escort fighter ... just the boosted ailerons to make a good warm-climate/low alt fighter though)
One possible workaround for the funding difficulties would have been licensing/adapting existing auxiliary supercharger technology from P&W, or at least using it to accelerate Allison's own development (and avoid delays with half-hearted 'cheap' attempts at repurposing the same integral supercharger housing+impeller into an auxiliary stage, among other things Allison tried initially). Particularly the pre-war developments for the R-1830 (which should have fit the mass flow and pressure requirements of the early V-1710 rather well, likely matched with the 7.48:1 integeral stage speed intended for low-alt and turbocharged installations). Work to allow either rear or side-mounted auxiliary stage orientation (or perhaps even under or top-mounted) would improve flexibility of installing such engines on existing designs using single-stage engines. The V-1710 was specifically designed for modular accessories, so having that sort of flexibility really should have come with the territory.
ADI/water injection is useful, but given the research and testing necessary for addressing concerns over corrosion (especially when used in combat -ie relatively recently before landing, not just on take-off) and required bulk/weight of an ADI fluid tank (again, reduced for use on-take-off only) makes this less attractive than intercooler development. I'm not sure if the R-2800 had operating limits for water-injection use to this effect or not, but the relatively early-ear introduction of that mechanism seems like it might have been initially limited for take-off purposes (akin to that on the Bramo 323R-2). For carrier or short airfield use, that added boost on take-off could be critical, especially for long-range or fighter-bomber missions with heavy external loads.
Edit:
Found the discussion on crankshaft variations
Curtiss-Wright: Loss of Don Berlin and downfall
According to "Vee's for Victory" there were 4 'different' crankshafts used in the Allisons. The first 3 look identical, at least from a distance. I don't work on them so there may be minor visual clues. The first were 'plain' crankshafts which I believe the C-33s got. The next version was shot peened, different surface texture? much improved fatigue life. I don't know when it was introduced. Then they nitrided the crankshafts in addition to the shot peening. This allowed for another major increase in fatigue life.
Each step allowed for roughly an unlimited life at a stress level that the preceeding step would only tolerate for a very short period of time. Nitriding was introduced in early 1942 and allowed about a 70% increase over the old plain steel (not shot peened) Crankshaft in stress levels for the crankshaft with both cranks operating at a level that they could sustain for an unlimited duration. Also in 1942 the casting method for the engine blocks changed. The new method required about 10% fewer operations to manufacture ( casting was closer to finished dimensions), weighed a bit less and was stronger. There may have been changes in the vibration damping system between the "C"s and the later engines. Or between certain models of the later engines.
The "C" series engines, according to the book, were rated at an overspeed of 3600rpm. The "E" and "F" engines were rated at 4100rpm for overspeed when introduced and the "G" series with the 12 counter weight crank was rated was rated in excess of 4400rpm.
This was not theory. As part of the engine type test the engine had to survive running at that speed for 30 seconds and do it a number of times during the duration of the test, usually a minimum of 10 times, depending on contract.
Now what happened in the field could be way different and what an individual pilot did either in pursuit of an enemy nearly in his sights or when trying to save his own life could be different also.
However, trying to operate "C" series engines at power levels used by "E" "F" engines, while possible short term, was at a lot higher risk and definitely shorter engine life, let alone the reduction gear problem.
The US Air Corp had the problem of rating engines for combat use with the factory 3000-8,000 miles away from the front lines. Spare engines and spare parts for even an in theater overhaul shop had to be transported those distances. They had to trade off short term performance gains of the aircraft vs blown engines, making men fly planes with engines in questionable condition, not having enough planes in service to fly the desired number of missions in a day and so on. Which more hazardous to a pilots life, not being allowed to use WEP settings and flying in a 12 plane formation to meet the enemy or being allowed to use WEP settings and having an 8-9 plane formation to meet the same number of enemy aircraft?
Maybe they did get it little wrong, maybe they got it a lot wrong.