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.
How to Win Friends and Influence Nazis - S3-E7
Deliberate mistake: Burkhalter pulls some papers out of his bags marked "Top Secret." Why would German papers be marked in English, so the prisoners know what not to look at?
Hogan's Trucking Service... We Deliver the Factory to You - S4-E4
Deliberate mistake: When Schultz drives off with the motorcycle leaving the sidecar behind, you can see that the sidecar has been propped up. It has to be, or it would fall over. Sidecars, bringing only one wheel to the party themselves, can't stand up on their own.
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.