Factual error: Burkhalter refers to Jesse Owens winning the gold medals in the Berlin Olympics, and that Hitler left the stadium every time Owens was to be presented a medal. Truth was, Hitler left the stadium when another black man won the day before, and didn't snub Owens at all. In fact, Hitler wasn't in attendance the days Owens won.
Factual error: In several episodes, the fence around the cooler is visible, and hanging on it, a sign saying "Eingang verboten" meaning "no entry." The correct German term would be "Zutritt verboten." In German, "Eingang" is the opening where you enter a building, not the act of entering one.
Factual error: When the crew in the plane gets ready to drop the bombs on the refinery, Hogan (in the pilot seat) tells Carter (who is looking through the bomb sight) exactly when to push the button. In fact, the pilot of a WW2 bomber had no way of even knowing when exactly to release the bombs - it was the job of the bombardier, looking through his targeting optics, to know that. Carter at the bomb sight should be telling Hogan how exactly to steer to get the bombs onto the target.
Factual error: The "Blue Baron" tells the dancer that the Kaiser gave him a certain medal. In fact, the medal he points to (and the girl fondles) is a WW2 repeat badge to the Iron Cross first class, instituted in 1939 to denote presentations of the Iron Cross first class to personnel who had already received it in WW1. He may have received the original Iron Cross from the Kaiser, but by the time he had a chance to receive that repeat badge, the Kaiser was long through handing out medals.
Factual error: Klink and Hogan sit behind each other in the P-51 they try to steal. The P-51 is a single-seat airplane, the only twin-seat P-51 are trainers. A trainer would not be at the flight line with the regular airplanes, and if a trainer would actually scramble with the others, it would at least arouse suspicion.
Factual error: While the barracks were reasonable replicas of the real POW barracks, there was one main difference. The original buildings were elevated to ensure any escape attempts could be stopped. In this series, the barracks are flush on the ground, which makes the tunnel access possible and easy.
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Factual error: A sharp brass cone has been put over the spike on Klink's Pickelhaube, so Hogan can pin the page torn from the Geneva Convention onto it. The real spike of a Pickelhaube has concave slopes, and it isn't pointy enough to pin a piece of paper onto it.
Factual error: In the tunnel Hogan loads a magazine into a US issue .45 pistol and points it at Myra, but he never chambered a round and didn't cock the hammer on the pistol. The .45 pistol in WW2 was single action. For a single action pistol to fire, a round needs to be chambered and the hammer has to be cocked manually before the trigger is pulled and the pistol to fire.
Factual error: Hogan calls the radio detection truck "radar" when he orders the SS guard to switch it off. From other episodes, we know that Hogan knows what radar is, and back then, the difference between radio homing equipment and radar was even clearer to people than it is today, because radio homing was an established technology, while radar was brand new, and most people were not even aware it existed.
Factual error: Baker picks up a lot of static in his radio, then suddenly signs off and says "Sounds like the radio detection unit picked up our signal." Unlike radar, radio signal homing relies entirely on measuring the signals emitted by the transmitter that is tracked. It works by comparing the strength of the signal arriving at each component of an array of directional antennae. The process is completely passive and does not cause any alteration of the signal measurable at either receiver or transmitter at all, and certainly not any audible interference or humming.