Rationalising production (fewer types) and training (a greater number of less elite pilots) seems obvious if not much fun.
Can you improve the engines? 18-cylinder radials are hard. Everyone was trying but only the Americans really got a lot of use out of them during WW2. If you're stuck with 14-cylinder the Kasei is pretty good. The Kinsei and Ha109 are not bad but a little small. Possibly some rationalisation here also - too many small engines which sucked up resources but were just not powerful enough by mid war. (Like Bristol - just focus on the damn Hercules and Centaurus!) The
Mamoru might have been good if they could make it reliable.
Japanese have had a decent production of 18 cyl radials. Homare was a victim of ever-lower production and maintenance standards as the war was closing to the end, as well as fuel octane number not guaranteed to be 91/92 oct (me, I'd go with compression ratio of 6.5:1, if not of 6:1 instead of historical 7:1, in order to be still useful on lower-octane fuel). The Ha-104 was not used on fighters, so there is a missed opportunity. Both of the engines were made in few thousands - not that great when compared with 'Western' production numbers of ~2000 HP engines, but still an useful number.
Ha 109 was excellent, (un)fortunately Japanese failed to take advantage of the design and upgrade it, even if it is just addition of water/alcohol injection. Kasei was also very good, Japanese managed not to make an useful fighter around it ( Raiden was too late and too few to matter)
Yes, the small engines, like Zuisei and Sakae were over-produced.
The DB 601 licence production in two factories was the money
not wisely spent, either.
2-stage superchargers? If you want to intercept B-29s you need altitude performance and they were trying but not very successfully (like the Germans). Again, this is hard. Were they missing anything obvious?
2-stage superchargers were known to work well at high altitudes already by mid-1930s, so yes, they missed the obvious.
Airframes? I don't think they did badly given the engines they were using. The A6M2 in particular is incredible for only 950hp. Could use a bit of tweaking in favour of high over slow speed manoeuvrability, but they were onto that pretty quickly. Probably the A7M was too ambitious a successor, they needed an intermediate with a 1500+hp 14-cyl rather than a 2000+hp 18-cyl (I don't know if the A6M8 would have worked out). The Ki-44 is also good but not a carrier plane and a bit short ranged by Japanese standards. I don't know as much about bombers/recon but what tradeoffs are you willing to make (other than having fewer specialised types in the interests of greater production)?
Excellent call on not making the number of specialized types.
Zero needed major engine upgrade at least by mid-1943, so it can sport all the requirements of the modern ww2 fighters: protection, performance and firepower. Kinsei or Ha-41/-109 would've looked just fine on the Zero, so don't wait until 1945 for the nose surgery. In the meantime, have Mitsubishi, Kawanishi and Nakajima work on the next-gen carrier-borne fighter, instead of Raiden, Kyofu and Gekko, respectively; no Saiun, install the cameras on other fast naval A/C.
Ki 43 needs to be replaced in production by mid-war; even a Sakae-powered Ki-44 is an improvement.
Kawasaki fighters' types - Ki-45 used twice the material resources and fuel when compared to Zero for no gain; Ki-60 and/or-61 with Japanese radials already in 1942 would've been just fine.
Armour/armament? Arguably a weak spot but with limited horsepower you face some tough choices. If you want to protect against .50 cal the armour and particularly the
self-sealing tanks have to be so heavy you are trashing the performance of early war 1000hp planes, as the Americans found. And if you give up range you give up a lot of the early war victories. Yes to 20mm cannon or HMG a bit earlier on the Oscar.
Greater emphasis fighters with on better engines early on - Kinsei, Kasei, Ha-41 - would've enabled the Japanese to have their cake and eat it, too.
A belt-fed Type 99 by 1941 (or at least the 100 dr box for it) would've been a boon for the Japanese.
Both their air forces did about as well as you could ask for at the start of the war. How much could they have improved in the next couple of years before they got completely swamped? I'm really not seeing a lot of plausible opportunity for qualitative improvement except maybe getting a Ki-100 (or less specialised J2M? Shiden or Hayate with Kasei instead of Homare?) type plane with carrier capability a couple years earlier. Not much in the big picture, which is a country punching hopelessly above its weight. As I think I wrote on the German thread...
Focus on bigger radials ASAP, so the small radials by Nakajima and Mitsubish are not much less needed. Have Kawasaki and Aichi continue to make radials in ever greater quantities instead of DB 601s. Both air services would've been fielding the 370 mph fighters by 1942, with protection and good firepower. Don't waste time and resources on floatlplane-this and -that (makes Kawanishi delivering useful aircraft by 1941).
Licence-produced Fw 190 (with Japanese engines, guns etc) would've been a boon.
All of that needs to be backed-up by wide introduction of radars and greater emphasis on greater number of new pilots.