I Look Better in Basic Black - S1-E28
Factual error: The American women the SS brings into camp claim to be entertainers having performed for troops. The series is allegedly set in 1942. Before June 6th, 1944 there were no allied troop concentrations in central Europe, certainly not in Germany, and very certainly none of a size and security rating the USO (or probably rather its predecessor organization, since the USO was founded in 1941 and would not have been fully operational yet) would send a troupe of female entertainers to.
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.
Plot hole: The prisoners fake a fire with some smoke bombs to have an excuse to rush into the print shop and smash up the print plates. Afterwards they even receive thanks and a reward for their valiant efforts. In reality, the guards would notice immediately that nothing in that room is even singed, but everything important has been smashed by fire axes.
The Antique - S5-E12
Character mistake: Schultz states "In Hammelburg, they call me die Glitterzehe", which is a literal (but wrong) translation of the term "twinkle toes." That term does not exist in German, and even if it did, it would have to be GlitZerzehe, because the German word for twinkling is 'glitzern', the word 'glittern' does not exist.
Visible crew/equipment: As Hogan and Carter approach the staff car, the crew and film equipment are reflected on the chrome of the lights and radiator.
Other mistake: The men are usually all wearing boots. When Carter goes up the ladder, it's clear that he has high-top sneakers on.
Praise the Fuhrer and Pass the Ammunition - S2-E19
Factual error: In the ammunition dump, a sign saying "Warnung Hoche Sprenggefahr" can be seen. That is not correct German. First, and foremost, it must be "hohe" and not "hoche", the latter form does not exist. Secondly, the word "Sprenggefahr", while not formally wrong, was never used in German. Depending on what the meaning of the sign is supposed to be, it must either be "Explosionsgefahr", if the overall danger of an explosion is meant, or if the property of the ammunition of being explosive is meant, it should be "Hochexplosiv." If the general presence of explosive material is being warned of, "Explosivstoffe" or "Hochexplosives Material" would be possible.
Revealing mistake: When Le Beau holds up the gold painted brick and the "gold" brick, the ends reveal that they appear to be pieces of lumber. The ends seem to have grains consistent with lumber.
Factual error: Erica says she has a plane to take Klink and her to Argentina. The only transatlantic airplane in Germany at that time was the FW-200 Condor, whose military value would have made it hard to requisition even for an SS Gruppenführer (which would be the real rank a "General" would hold in the SS, different mistake), let alone for his wife. Plus, even the FW-200 could not have made it even to the Brazilian coast without a refueling stop somewhere along the African west coast, which would have been a problem, because Germany had no possessions there. Klink, being a Luftwaffe (Air Force) officer, should have at least been suspicious of that plan, even if he didn't know all the details off the top of his head.
Request Permission to Escape - S1-E32
Character mistake: When ordering Schultz to finish cleaning his car, Klink salutes Schultz, his returning the salute with the garden hose in his hand leads to Klink being soaked. A salute is, except in rare circumstances, always initiated by the lower-ranking individual and returned by his superior, not the other way round. This rule is broken especially by Klink in several other places as well.
Movies Are Your Best Escape - S1-E8
Revealing mistake: When Schultz is talking to Hogan and Le Beau, the guard outside walks past. As he does, you can see three shadows from him revealing the studio lighting, rather than him really being outside.
Continuity mistake: When the staff car is approaching the fallen tree it has white staff flags, but when it stops at the tree it has the red swastika Nazi party flags. (00:12:00)
Hogan's Trucking Service... We Deliver the Factory to You - S4-E4
Audio problem: When Crittenden is figuring out military time he asks Hogan how much four and six are. The answer doesn't match Hogan's lips.
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.
The Battle of Stalag 13 - S2-E5
Revealing mistake: When the scene transitions from Klink and Hogan to a night shot outside of the barracks, you can see palm trees above the roof line. Not normal for the area that's supposed to be represented.
Everybody Loves a Snowman - S3-E14
Continuity mistake: Carter and Newkirk have just taken the escapees down the tree trunk to the tunnels. When they go to open it, they clear off the snow to open it. When the shot goes to a German soldier that was chasing them, the phony stump is suddenly covered over again. It would still have been visible, having just been exposed.
Heil Klink - S2-E22
Other mistake: When the camera pans left following Brauner's car, you can see palm trees in the background. The area the Stalag is supposed to be in wouldn't have palm trees.
Plot hole: The boys take out the radio control unit from the mini tank. Le Beau is needed to get in and drive it to make it appear okay. After going between the buildings, they get him out, and start it on its way. Trouble is, no remote control and no driver, yet it turns and operates smoothly.
Revealing mistake: In the close ups of Maj. Zolle, it can be seen that the spectacles that he has on have no lenses.
Continuity mistake: As Schultz marches in with the Kraut platoon, he reports to Klink. As he goes to stand at attention and report, the new tunnel section he's over collapses, and he completely disappears into the hole. The camera goes to a close up on Klink, then back to the hole, and you see Schultz standing in the hole and it's only chest deep.
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.