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: In many episodes, SS members of all ranks appear - the most notorious recurring character being Major Hochstetter. Curiously enough, Hochstetter couldn't have been a Major in the SS, simply because that rank didn't exist there. The SS used the SA rank system, not the Wehrmacht one. Hochstetter for example would have to be a Sturmbannführer. Colonel Feldkamp would have to be a Standartenführer. To avoid confusion: Hochstetter sometimes claims he is Gestapo, even when he's wearing an SS uniform (different mistake). However, he couldn't be a major there either - he'd have to be a Kriminalrat or Kriminaldirektor, because the Gestapo, which was in principle a civilian police organisation and wasn't half as closely integrated with the SS or the military as the series would have us believe, didn't use military ranks at all.
Character mistake: In several scenes all over the show (though not always!), characters use the command "Raus!" to send somebody away from somewhere. Raus, short for "heraus" literally means "out" in the sense of "out of a building", which would be "aus einem Gebäude heraus" in German. Used as a command, it always means "get out", never "get away from there" or "get lost", in other words, the addressee must be inside of somewhere to be ordered "Raus." One example would be Schultz sending the prisoners away from general Burkhalter's car in S05E13.
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.
Factual error: Baker and Kinchloe, the radio experts of the troupe, often use Morse code to communicate by radio. When they do, they hammer the Morse key in different intervals, but always just barely tap it. Morse code is made up of "short" and "long" beeps. To produce a "long" in Morse code, you have to hold the key down three times as long as you would for a "short". A tap would be a "short" - the beeps they are sending are spaced long and short, but that's not how Morse code works.
Other mistake: Throughout the show, they always show snow on the ground and ice on the windows. It is almost always freezing weather. They regularly use a periscope viewer that is placed it a 55 gallon drum containing water, yet the water never freezes or shows any kind of icing up.
Continuity mistake: Throughout the whole series, the guys access the tunnels through a trapdoor built into the bunk closest to what appears to be the east end of the barracks. What is interesting is the method used to make the trapdoor open and the bunk rise. sometimes, it's two taps, two slaps, or two pushes of a "key", a panel that's made to look like the side of the bunk.
Character mistake: During the opening scene of every episode, Klink comes out of his office and salutes. Then it cuts to Sgt. Shultz who then salutes. The superior officer never salutes first, it's a sign of respect of rank. There is one exception for this in the American military where if the soldier is a Medal Of Honor recipient, the superior officer will usually salute first but is not required to.
Audio problem: In several episodes, e.g. S1E31, German police sirens are heard to underline the impending arrival of Gestapo or other police officers. In each occurrence, the sample used has a distinct Doppler effect. Doppler effect in a sound occurs only if a vehicle passes by the listener at high speed, not when a vehicle approaches a place directly and stops.
Factual error: Numerous times throughout the series, there are palm trees seen in different shots. Stalag 13 was supposed to be just on the outskirts of Hammelburg. The only place anywhere near there that could support palms was the area around the Bodensee (Lake Constance), so therefore the palms seen are a big mistake.