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.
Deliberate mistake: The film crew did not always bother to switch out the rank insignia on the uniforms of extras. In this episode, that leads to all kinds of enlisted and noncom rank insignia being present in the lineup of brand-new recruits when Klink inspects them. Rightfully they should all wear a single eagle on a borderless patch of a Flieger on their collar.
Other mistake: The scene in Klink's quarters is one of a few where you can see Larry Hovis' (Carter) wedding ring.
Continuity mistake: After Hogan, LeBeau, and Newkirk leave, Carter is sitting, holding the glass with both hands. After the cut, he's holding the glass in his right hand only.
Continuity mistake: When Hogan and the crew first see the silent airplane overhead, it has a twin tail. When shown up close in later scenes it has a single tail.
Continuity mistake: After getting Crittendon to turn around, Hogan grabs his hat with his right hand. When the camera looks at Hogan, he's pulling his left hand back, holding his hat.
Some of Their Planes Are Missing - S3-E2
Visible crew/equipment: When LeBeau, Carter and Schultz enter the visiting Germans' quarters, when the door is open you can see the sound stage floorboards are uneven in front of the door to the neighbouring barracks.
Two Nazis for the Price of One - S3-E17
Continuity mistake: Freitag is shot at night, but when Hogan goes outside and talks to his men it's daytime.
Everybody Loves a Snowman - S3-E14
Revealing mistake: As the sink with the fake tunnel is prepared, just before Newkirk goes over to set things up, you can see movement through a crack in the door. It's Schultz, Hochstetter, and Klink, waiting their cue to enter.
Continuity mistake: After Hogan leaves the airman in the tree, LeBeau jumps down, and looks up to tell the man it will be OK. When the camera looks at the man, you see LeBeau's legs and feet behind him.
Top Hat, White Tie and Bomb Sights - S1-E10
Audio problem: As Schultz is complaining about Klink, Hogan puts his hand over Schultz's mouth, and you start to hear the canned laughter. When the camera looks at Klink, the sound Schultz made with the canned laughter behind it is repeated.
Request Permission to Escape - S1-E32
Other mistake: Carter is washing things in front of the barracks. There is snow on the ground and on the windowsills and they are wearing winter jackets but the cold weather doesn't bother him putting his hands in the water over and over. He even gets splashed in the face but it doesn't faze him.
Continuity mistake: The scar on Burkhalter's right cheek changes location, relative to the mole on that cheek, in every episode. Possibly in every take.
The Great Impersonation - S1-E21
Plot hole: This episode revolves around training the reluctant, untalented Schultz to impersonate Klink to get the captured heroes back from the Gestapo. This is actually a pretty common theme, somebody, usually one of the heroes, impersonating an officer to free a prisoner. The plot gives no reason why this time, they would have to use the cowardly, untalented Schultz instead of doing it themselves.
The Kamikazes Are Coming - S6-E20
Factual error: When Hockstetter shows up in Klink's office he has two SS soldiers with him. One has a coat on with a general's rank insignia.
Funny Thing Happened on the Way to London - S3-E5
Plot hole: When the driver of the car addresses Roberts (the real Roberts that is, not the double), Roberts reprimands him, telling him not to call him Baumann. It is safe to assume the guard was supposed to be speaking German, since he addressed Roberts by his German identity. That poses some interesting questions. Did Roberts speak English? In those days, most Germans did not even have a basic knowledge of the English language. Did he speak German? That would imply he has a good enough command of the German language to pass as a German. Roberts however isn't a spy like Hogan and his crew, but a pilot in the RAF.
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.