I think in the instance of the Battle of Britain, the mistakes were made by the Luftwaffe in this case, since although devastating, sustained attacks against 11 Group's airfields were not consistent, nor as thorough as they could have been. Obviously the RAF squadrons dispersed, but many of the airfields bombed were back to being in use again within days of the LW attack. The Germans also lacked in effective recon, so they were never able to assess accurately what damage was being done and where, nor were they able to establish an accurate picture of how they were doing - one of their biggest failings of the Battle.
They were not that devastating. The key thing was that the fighters were not caught on the ground and destroyed there. Taking out airfields of that time, with planes that were quite happy to land and takeoff on grass was really difficult if not impossible. Plus there were many alternative airfields all over the place.
For the Luftwaffe to win they had to achieve a kill/loss ratio of about 4:1 in fighters, at least, since they still had to have some 109s left for air cover for an invasion (5:1 was probably more realistic) as Britain had a lot of bombers.
There was only one sure fired way of doing that ... catch lots on the ground and destroy them. The Luftwaffe were very aware of this, they were very careful to camouflage and protect their own airfields in France, as British bombers found out to their cost.
Park made sure that never happened. What a delicate dance he played, intercept and inflict the maximum damage all the time, while always ensuring he never got caught out. Day after day, month after month. A lesser man would have failed (eg LM).
Dowding and Park knew they were in a war of attrition and played to that accordingly, the Luftwaffe didn't and lost as a result. After so many 'quick cheap wins' they were not prepared (or was the German economy) for that sort of battle.
Plus the RAF's command and control system (forever more called the Dowding System) was a thing of rare beauty, effective, fast, high levels of redundancy, et al. Plus it was designed for human mental strengths, it was visual with simple symbols to denote what was happening and enhanced, what the human brain is really good at, pattern recognition.
This enabled someone competent, such as Park, to respond very quickly as the Luftwaffe continually changed tactics and targets.
The Luftwaffe are never given enough credit for how flexibly they thought and tried out new things and tried continuously to 'con' the RAF into the wrong moves. This was no lumbering behemoth, they probed, they changed targets, they changed tactics, they always tried to get the RAF into fighter traps. Yes they were limited in information, but that didn't mean they weren't creative and smart. Against a lesser opponent they would have succeeded.
As for the 'Dowding System'. Even today, with all our computers and communication abilities there are very few (any?) systems as effective.
Very, very, very few people really understand good C&C systems properly, the list of rubbish and disasters is far (far?) longer than the list of successes. Here in Victoria Australia, we created a 'state of the art' C&C system for (mostly) bushfires. When "Black Saturday' hit us ... it progressively fell further and further behind until it was a couple of hours behind reality, whole towns were wiped out before the 'centre' even knew what was happening and the orders they were giving out were nonsense (and downright fatal in some cases) as a result ... so much for technology and stupidity (note that modern tech can allow people to stuff up even faster and more effectively than before, a real double edged sword).
In one sense it was sheer luck that the British won. If Leigh Mallory had been in charge of 11 Group ... or Sholoto Douglas had got his 10 (or was it 20 he wanted) squadrons of Defiants.
It was luck that Dowding was able to survive in a hostile (and very political) RAF and create the components and the system.
Luck that Park was in charge of 11 group (thanks to Dowding again) .. a New Zealander for that job?
And luck that Chamberlain (never given a good press) was so supportive of fighters, which went against everything the RAF and Air Ministry stood for.
And lucky for the RAF, which has ever shone in the glow of the BoB, wiping out it's many, many, many stuff ups during the war (and seemingly ever since).