The 43rd, a Moving Story - S1-E23
Other mistake: When Hogan uses the water barrel periscope to spot Manor Kuhn, the first shot is from an impossible angle.
The Late Inspector General - S1-E4
Other mistake: While the General is in Klink's office making the recommendation for Klink to be commandant of all German POW camps, he mistakenly calls Stalag 13, Camp 13 three different times. Camp 13 was referenced in the black and white pilot episode.
Suggested correction: Stalag is short for "Stammlager." "Lager" is the German word for "camp." (To avoid unnecessary discussions: depending on the context, "Lager" can also mean stash, cache, storage, warehouse, bedding or bearing, but in this context it is indubitably to be translated as camp). So "Camp 13" is absolutely correct in this context.
Oil for the Lamps of Hogan - S1-E14
Plot hole: The Heroes take an empty oil drum to the depot, knowing full well that Schulz will protest, allowing them to steal a full one. However, all but their barrel have snow on it. Since it's really salt, it all falls off as they load it on the cart. With real snow, that wouldn't happen. It would be quite obvious that the barrel they are taking out is not the one they brought in.
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"?
Factual error: Hogan mentions a store that offers "thirty percent off on T-shirts." T-shirts were mostly unknown in Germany during the 3rd Reich, and didn't see widespread use before the 1960s. Before that, the traditional Unterhemd, known in America as tank top or wife beater, was worn almost exclusively.
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.
Plot hole: Hogan's men steal the motor from the silent plane. When Klink and Burkhalter inspect the plane, Burkhalter doesn't notice the engine missing. Later Klink doesn't notice the fact that it has been put back. This is totally impossible for two reasons: Firstly, if a propeller airplane misses its motor, there is no place to mount the propeller. Secondly, when we get to see the whole plane, it becomes obvious that it has an open engine cowling which leaves the motor exposed to be cooled by the airstream. The propeller issue aside, if there is enough light to see the hand in front of your eyes, it is impossible to miss either the presence or the absence of an engine inside that kind of cowling. Add to this the fact that both Klink and Burkhalter are Luftwaffe (Air Force) officers and therefore by trade have some experience with airplanes, the whole thing becomes even more ridiculous.
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)
The Great Impersonation - S1-E21
Factual error: When the three captured heroes stand before the Gestapo officer, he sweeps three sets of US identification tags into his hand. The names and uniforms suggest that the three captured personnel are from three different armies. Identification tags differ greatly between armies, all wearing US-style with their usual uniforms they would be worse off than wearing none at all. The Geneva convention would allow for them to be shot on the spot as spies under these circumstances since they initiated combat (blew something up) wearing false uniforms. (00:03:20)
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.
How to Cook a German Goose by Radar - S1-E24
Revealing mistake: When the boys set the trash can on fire in front of Klink's office, there is a problem with the trash. While the rest of the waste paper burns down there is one piece hanging over the top edge that doesn't burn, even being in the midst of the flames on that side.
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.
Other mistake: The truck was stashed behind Hogan's barracks. The Kommandant's office was on the other side of the building. While stealing the boxes of gold, there would be no way that the POWs would have been able to see any approaching figure.
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.
Other mistake: After Shultz herds the prisoners into the barracks, Hogan opens the door and motions to Newkirk in the tank to get going. Problem is, there are no side viewports for Newkirk to see Hogan, and it looks like he motions to the camera. Also, Shultz is at the wrong end of the building to see the tank go into the end of the barracks.
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.
The Informer - S1-E1
Other mistake: Klink has on his monocle, as usual. If you look closely, the monocle is a single lens, with no frame. From Episode 2 onward, the monocle has a frame and a gallery. Also, Klink wears it at an angle, not unlike the Penguin in the original Batman series, who also wore a monocle without a frame.
Anchors Aweigh, Men of Stalag 13 - S1-E16
Factual error: When Shultz is standing at the top of the ramp with a crate marked "hors d'oeuvres", talking with Carter and Lebeau, if you look to the right of Shultz's head (camera's left) you can see the Desilu Studios water tower.