Well, let's be Frank, everybody makes mistakes and sometimes those mistakes can lead to dire situations and when it comes to warplanes mistakes should be a big no-no. And in a war like the second world war there were plenty mistakes made because of haste in pushing something untested into service or something clearly obsolesent because of outdated military protorcol or out of pure greed.
The General Motors Allison V-1710 engine was the victim of the latter.

The only US built V 12 engine was riddled with problems concerning its service ceiling and when fitted with turbo chargers they were not properly synchronised with the RPMs of the engine. So it was either, fly below 15,000 feet or face the increased problems brought on by addition of the turbosupercharger. To it's credit, the Allison V-1710 was a tough engine, it could survive being shot to bits and bring the pilot back home, it also was an easy to maintain on the battlefield engine, since replacement parts were exact fits because of being line produced. So why was this engine a victim of greed?
First of all, since it was a General Motors product it could be build in big numbers on their big production line whereas comparable European made engines such as the Rolls Royce Merlin, the Daimler DB-605 and the Junkers Jumo 213 were largely made by hand, the USAAF's high command and the big bosses of General motors were keen to show that their production line build engine could perform just as well as those largely handmade engines of their competitors. And as such the Allison was put in a LOT of airplanes, which were flying billboards for the USAAF and General Motors. The Allison powered among others:

The Curtiss P40 warhawk.

The Lockheed P38 Lightning.

The North American P82 Twin Mustang.
But probably the most notorious of all.

The Bell P39 Airacobra.
Now back in 1939 when NASA (Then known as NACA, National Advisory Committee on Aeronautics.) was reviewing the prototype of the Bell P-39, the plane had been given a turbo-supercharger to make the most of what the engine had to offer. Believing that an improved version of the Allison V-1710 was in the latest stages of development, the NACA told the high command of the Army Air Force that the Bell P-39 should NOT be fitted with a turbo-supercharger when in fact it would take four years before that improved version of the V-1710 became available, at which more advanced aircraft would be getting that engine.
So with that recommandation, the pilots who went to battle in the Bell P-39 found themselves flying an underpowered, severely restricted plane, unfit to do battle with Messershmitt 109's or Focke-Wulf 190, who quickly caught on that the way to get away from a P-39, all you needed to do is just fly up, above 20,000 feet, where the P-39, could not follow.
Hundreds of pilots found their death in the Airacobra thanks to NACA's insistance of deleting the Turbo-supercharger. However, the Airacobra redeemed itself in Soviet Service where it was used as a low level strike aircraft, the Russians bought and flew Cobras in their thousands in that role and it was praised for being sturdy and providing something that indiginous Soviet combat planes didn't have: Radio.
Another aircraft, like the Airacobra, that entered service without having been properly tested was the Curtiss SB2C Helldiver.

Intended to replace the aging Douglas Dauntless divebomber on carriers, the Helldiver had some pretty big shoes to fill. The Dauntless was a tough , dependable and easy to fly plane, which overcame tremendous odds. The Navy required the successor to be more heavily armed, it could carry a bigger load than the Dauntless, it also needed to be faster, more powerful than the old Douglas.
In that aspect, the Helldiver gave the Navy exactly what they asked for but even during flights with the prototypes test pilots found that the Heldiver had a notorious ballance problem with a weak tail surface and it was extremely difficult to pull out of a dive, which for a dive bomber is essential, without ripping the tail clean off. Also when tested on carriers pilots found that the Helldiver's landing speed was far too fast to guarantee a safe landing and once again that the balance problem made the aircraft top-heavy. And if that wasn't enough, the weak tail surfaces often led to the tail snapping off on impact with the carrier deck.
British pilots were even harsher in their verdict: they wouldn't go near a carrier with the Helldiver, in their eyes it was unsuited for carrier use, nevermind for use as a divebomber.
Ragardless of that and with the war in the Pacific escalating the Helldiver was pushed into service and began to replace the Dauntless as intended. But the pilots and crew of the carriers which operated the SB2C weren't too happy with their new toy, most of the helldivers which got lost during the war found their end in landing accidents or when the tail broke off during a dive and after a while the SB2C got the nickname "Son of a Bitch Second Class"

a very dramatic picture of a typical Helldiver landing. Note that the aircraft has already spun 180 degrees and that one of the legs of the landing gear has broken off and is actually captured while in mid air.
After the war, the SB2C was quickly replaced by the much more capable Douglas AD1 Skyraider, which like the Dauntless enjoyed a long service career and affection from those who flew it.
Okay these were American airpower mistakes but they weren't the only ones, the reasons why the Blitzkrieg was succesful for the Germans was of many of those countries they invaded stubbornly held onto obsolete military protocols.
Having Biplanes as frontline fighters in one example, the Gloster Gladiator and the Polikarpow I-15 were widely exported. Because of the militairy protocol dictating what a fighter aircraft should be like: Light and agile, because that's what gave WW1 fighters like the Fokker D-VII the edge here: they could outturn everything in the sky.
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The Gloster Gladiator

The Polikarpow I-15
But it wasn't just biplanes that ruled the roost, there were monoplanes around it was just that... Well see for yourselves and make your own judgement. I'll name a couple and some trivia about them.

These are Fokker D-21 fighters of the Royal Dutch Army air force.
The D-21 was Fokker's first monoplane fighter, but sticking to protocol, it had a non-retractable undercarriage, and was made using the tried and tested method of steel tubing and linnen fabric. To its credit, while slower than the Messerschmitt 109, the D-21 was a dependable workhorse that could pack a serious punch but many of them never even got airborne. (More about that later...)

This is a Brewster Buffalo.
With war looming, many companies saw money in offerring the rejects for sale for chips. The Buffalo was one such occasion, it was meant to replace the old US Navy carrier borne Biplanes but the design lost to the Grumman F2F Wildcat. But with war looming in Europe and with Air Forces desperate for new planes , Brewster aviation decided to not let those years in devellopment and priming the plant for production go to waste and offered the Buffalo to those needing air forces. But the Buffalo didn't have sufficiant armour, was too lightly armed and was too underpowered to pose a serious challenge against the Messerschmitt and the Japanese Zero. Many air force who bought the Buffalo found out in a painful way that there was a reason why the US navy rejected the plane in the first place.
As I mentioned in the description of the Fokker D-21, if it could get airborne it could put up a good fight, many of them didn't and that's because of another obsolete military protocol.

These are Wellington Bombers on a British airfield. Back then, planes were meant to be flying artillery, ready to be deployed at a moment's notice, as such they were always parked neatly in a row and it was that way pretty much all over Europe. They found out in a painful manner that parking planes neatly in a row also made it possible for an enemy plane to destroy them in a strafing run, many airforce couldn't get airborne in the first place because of losing their planes on the ground.
It was a combination of knowing those obsolete protocols and tearing up the rule book that gave the Germans the edge here.