Factual error: As the staff car comes up the street, there are a number of neon signs lit up, as well as store fronts. This is wrong as during the night in wartime Europe, such lighting would be dark to avoid night bombing.
Continuity mistake: As Hogan's telling Klink about the drawings, his left arm is extended. The next shot his arm is resting on the cigar box, then back to being extended and notice the pencil under the note pad. Next shot, arm is back on the box and pencil is gone. (00:04:45)
Other mistake: When the boys are working on the "jigsaw" map, Klink and the guard come in. There is a gust of wind from their entrance. Trouble is, the gust that blows the pieces comes from behind LeBeau, blowing the pieces toward Newkirk's bunk, rather than toward the camera.
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.