Other mistake: When Carter goes to switch the full cup for the empty one, he accidentally sloshes water on Newkirk's hand and the fan of cards in it. When Carter goes to move the cups, look at Newkirk's hand. The cup exchange happens in front of the hand. The hand is out of range of the water.
Audio problem: When Hogan is taking pictures of Shultz in front of the halt-track (really, getting shots of the control panel), in the second photo, the shot is shown as if it's Hogan looking through the camera. He starts on Shultz's face, but pans down and to the right to get the control panel. Just as the view gets on the panel, you hear the shutter click, just before the camera fully settles on the panel.
Revealing mistake: When the guys are by the half-track keeping Shultz busy, if you look just above and to the left of Shultz's head, you see some tall fencing at the top of the hill in the distance. From the set up, if appears to be a baseball field outside of the studio property.
Revealing mistake: When the men are in the yard during their exercise period playing football, there is a wide shot of the yard. The half-track is to the left of the screen with Shultz next to it. If you look above the barracks, the Desilu water tower and a large metal building, possibly a studio building, can be seen.
Other mistake: In the end of the episode, after LeBeau said "Hit the deck!", the camera looks to the half-track. According to the plan, there was to be a nitro charge inside it to blow it up. Watch the tarp toward the front. It twitches upward in response to a small explosion on the ground, rather than inside. The sound effects complete the illusion.
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.
raywest
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.