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.
Continuity mistake: After Burkhalter relieves Shultz of command, and Klink is reinstated, Klink sits behind the desk. On the blotter is a letter opener that Burkhalter was toying with, and a black covered notebook. After sitting, Klink reaches in his jacket pocket, pulls out the same notebook, and reads from it. The shot cuts to Shultz and back, and the book Klink read from is gone, (presumably back in the pocket) and the one on the desk is gone.
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.
Factual error: About 8 minutes into show, Major Hochstetter asks Schultz how long Colonel Hogan (an American) has been running the camp, and Schultz says 3 years last November. This is impossible. The US didn't get into the war until December, 1941, He would have to have been captured November '42 or earlier but the war was over by November 1945.
Plot hole: Five minutes into the show, Klink and Hogan are in Klink's office when a gestapo major comes in. When Hogan leaves, Klink mentions Hogan's name and the major realises with surprise that that is Hogan and then says he knows all about Hogan and his description. That alone should have led the major to know that this was Hogan. Hogan also has his name on a tag on his jacket.
Revealing mistake: When the men are in ranks for roll call, it's snowing heavily. Given the pitch of the barracks' roofs, there shouldn't be any snow sticking. Therefore, if looked at closely, it can be seen that the "snow" on the roofs is painted in place.
Continuity mistake: When Klink and Hogan are looking at the Mustangs, Hogan has just sipped his coffee and holding the mug at chest level, at the top button of his coat. When the shot changes, he's holding it waist high. Also, the flight line full of planes is a grainy black-and-white projection super imposed in the shot of the window.