Anchors Aweigh, Men of Stalag 13 - S1-E16
Continuity mistake: As Klink comes out to see the Officer's club, you can see Hogan is on the ground, and Kinchloe is on the boat by the shade. After a quick close up on Hogan, Hogan's suddenly on board, and Kinch has disappeared in a second.
Continuity mistake: When Klink does a walk through in the barracks, he turns to face Hogan in front of Schultz. As he does, the end of his riding crop pushes against Schultz's lower chest and sticks. When the camera cuts the crop is free and well clear of Schultz.
Go Light on the Heavy Water - S1-E9
Continuity mistake: The boys are looking out the window at the mysterious truck. When the camera looks at them from behind, there's a building right in front of them.
Movies Are Your Best Escape - S1-E8
Continuity mistake: Hogan takes the movie camera from Klink right side up. The next second, it's upside down. Then when Hogan goes to dunk the camera in the water, the lenses are pointing to his right. In the close up, they're facing his left.
Go Light on the Heavy Water - S1-E9
Continuity mistake: When the smoke bomb goes off, Klink has his monocle on. After the smoke really starts, his monocle is gone without being taken off.
Happiness Is a Warm Sergeant - S1-E11
Continuity mistake: When accessing the tunnel entrance, usually the spot is in the middle of the side board that is tapped. Newkirk slaps the corner and post of the top bunk.
The Informer - S1-E1
Continuity mistake: In this episode, the doghouse that disguises an entrance to the underground is flipped up on end, and the separate floor is flipped up in the opposite direction. In all of the following episodes, the doghouse, and the floor, are one piece.
The Informer - S1-E1
Continuity mistake: In this episode, Burkhalter holds the rank of Colonel, Carter is a Lieutenant. In subsequent episodes, Burkhalter is a General, and Carter is a Sergeant.
Oil for the Lamps of Hogan - S1-E14
Continuity mistake: Toward the end, Klink removes his monocle while talking to Hogan about the oil. Through the next few cuts between them, the monocle is off. When Hogan goes to leave, there is a shot from behind Klink, and he doesn't move, yet the next closeup of Klink shows the monocle in place.
German Bridge Is Falling Down - S1-E7
Continuity mistake: During his experiments to create explosives in the tunnels, Carter has a pretty extensive set of glassware on his workbench. Necessarily he would have to replace (most of) that after each explosion - not to mention various light bulbs, furniture and other non-blast-proof stuff by the way. A lot of that glassware is specialty equipment, it would not be easy to come by even one set of in peacetime for a free civilian. In wartime, for an allied prisoner (even with the heroes' connections) it should be nigh impossible, and totally impossible to have an inexhaustible supply of the stuff. So we can either assume a giant plot hole, or treat it (as I did) as a big continuity mistake.
Suggested correction: Considering they regularly get equipment of all kind air dropped from "London", a few laboratory instruments and containers would hardly be challenge.
Firstly, considering the number of explosions, it's not "a few" but more like "QUITE a few." Secondly, if they had had the option to receive airdrops at the time, they would just as have had them airdrop the explosives instead of the glassware for carter to blow up, wouldn't they? Or are you suggesting they would have more spare laboratory equipment in store than a wholesale laboratory outfitter, "just in case"?
The Safecracker Suite - S1-E27
Continuity mistake: As Schultz is asking about Alfie, saying "Who captured him, the Kaiser?", Hogan's hands are down. A second later, his chin is in his right hand.
Continuity mistake: Major Bonacelli goes to put his hand in his coat for money, he pauses with it in for the next few lines. When Newkirk asks about Germans eating a lot of pizza, Bonacelli's hand is suddenly out and gesturing.
Continuity mistake: As Schultz is telling Hogan that he's a family man, the shot ends with Hogan starting to turn his head to the left. The next shot shows Hogan looking straight at Schultz, then turning his head. (00:15:25)
Movies Are Your Best Escape - S1-E8
Continuity mistake: When Schultz herds the men into the barracks, Hogan and Le Beau are about three feet apart. A second later, they are only about a foot apart.
Continuity mistake: Newkirk holds takes Schultz's rifle so Schultz can play in the game. On Schultz's second hit, you see Newkirk clapping. In the close up, you see Newkirk's hands firmly on the butt of the rifle. Also, Newkirk is holding the rifle with the muzzle in the dirt. This would put a plug of dirt into it, but when Klink takes it away, you can see that the muzzle is clean and clear.
Top Hat, White Tie and Bomb Sights - S1-E10
Continuity mistake: As Burkhalter talks to Klink, he raises his hand for emphasis on a point. When the camera cuts to a wide shot, you see his arm down by his side, much too quick without a movement to relax the arm.
Top Hat, White Tie and Bomb Sights - S1-E10
Continuity mistake: When Hogan is looking around as Klink is showing the gate to Burkhalter. Hogan's hat is up on his head in the usual position. After the camera cuts to Klink, then back to Hogan, the bill of his hat is down shading his eyes.
Continuity mistake: When in Hogan's quarters, they're planning to steal a Tiger Tank from the Germans. When Hogan rolls up the map, the holder it's on magically slides back into the wall. Any other time, he has to push it back.
Continuity mistake: When explaining the "experiment" Lebeau has going, the multi-chambered tube is on the left (from the camera's POV) and the long tube with the coil is on the right. As the men up to leave after Carter comes in, the tubes are reversed.
Continuity mistake: After the POWs cut the stairs outside Col. Klink's office, Sgt. Schultz walks down them. There is a guard standing to his right. After a switch to show the POWs, when the camera goes back to the stairs, Col. Klink walks out and falls when the stairs collapse. The guard is missing without making any motion to move before. When everybody rushes to Col.Klink, the guard runs in from the left also.