Request Permission to Escape - S1-E32
Continuity mistake: While Carter and Klink's secretary are conversing, the waste basket Carter holds switches positions from up to down and back again.
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.
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.
Request Permission to Escape - S1-E32
Continuity mistake: As Schultz starts to wet Klink, several big spots appear on the left of Schultz's jacket, then disappear a moment later.
Answer: The core POWs regularly escaped the prison camp but they made it their mission to conduct espionage and commit sabotage in the surrounding German territory. They also collaborated with different underground resistance groups and used a network of secret tunnels to help prisoners from other POW camps to escape, who then relayed vital information back to the Allied forces. Hogan and his men maintained the illusion that Stalag 13 had never had any prisoners escape in order to avoid their covert operations being shut down. Being that the prison camp is set in Germany during WWII, there were no American embassies.
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Hogan has mentioned to different characters that they are actually stationed at Stalag 13 to help allied soldiers and prisoners from other Stalags to escape Germany.