Visible crew/equipment: Every time the boys use a flashlight to signal the planes, you can see the camera crew and equipment.
Factual error: While the show always made it winter time by having snow on everything (salt piles strewn about) and icicles on all the windows, this episode has an actual date of occurrence, June 6, 1944. They help to solve the snow on the set by taping the whole episode inside. However, the windows still all have the ice formations on them. It's late spring.
The Top Secret Top Coat - S2-E29
Factual error: In Klink's quarters, there's an (obviously fake) banana in the fruit bowl. Bananas were luxury items in Europe in the 1940s, and certainly so in war-torn Germany. The majority of Germans didn't have access to exotic fruit until the 1960s, and fake fruit of this type wasn't available then either.
German Bridge Is Falling Down - S1-E7
Character mistake: When counting the prisoners right at the beginning of the episode, Schultz counts to 15. However, including Hogan there are 19 men in formation.
German Bridge Is Falling Down - S1-E7
Continuity mistake: When we see the men lighting cigarettes, there are 25 people forming the arrow. When we are treated to an aerial view of it, there are 37 dots of light visible.
German Bridge Is Falling Down - S1-E7
Plot hole: We see Hogan's men empty out the gunpowder from a lot of cartridges inside the armoury. What did they do with their empties? It's not like a mound of empty cartridge cases on the ground wouldn't draw some suspicion is it? Yes, I am aware some options come to mind, e.g. putting the bullets back in and stuffing them back into the belts, but none of that is actually shown or talked about - LeBeau even chucks one cartridge over his shoulder, implying they are not very concerned about hiding their tracks.
Happy Birthday, Adolf - S1-E17
Character mistake: The artillery officer asks "Does headquarters expect a squad of infantry to replace experienced artillery men?" Hogan only offered "his detachment", and he's wearing a Luftwaffe uniform (and so is LeBeau). Why does the artillery officer get the idea that the "detachment" would be infantry, that is to say, ground forces (Heer) troops? To avoid confusion: Yes, the Luftwaffe did have infantry units, but those would be viewed by other branches as Luftwaffe guards primarily, not as infantry.
Continuity mistake: All through the episode, we are in a snowy, wintry camp surrounded by hills and trees. The target Gen. Burkhalter points out however is a little shed on a flat-as-a-board prairie with not a flake of snow OR a single hill visible anywhere, and the brown grass of late summer. (Yes I noticed there are some mountains off in the distance. So not relevant for this mistake).
Happy Birthday, Dear Hogan - S4-E26
Other mistake: Hogan returns to camp after meeting with the underground, after learning the Germans are setting a trap. Kinch went down in the tunnel to Radio London just before Hogan returned. Hogan asked the men, "Where's Kinch?" and he shouldn't send any messages. Since Kinch was in the tunnel, Hogan should have seen or heard Kinch in the tunnel using the radio. (00:07:50 - 00:10:45)
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.
Other mistake: Hogan is disarming a booby trap briefcase. The bomb expert tells him over the radio he has to decide to turn the handle clockwise or counterclockwise. The expert doesn't know which way to turn it. Hogan turns the handle counterclockwise and disarms the booby trap, and the expert says counterclockwise. There's no way the expert would have known which way Hogan turned the handle. (00:21:50 - 00:22:26)
Factual error: While introducing himself to the downed Russian pilot, Hogan claims he is with the "US Air Force." He was actually with the United States Army Air Corps (USAAC) as the US Air Force wasn't formed until 1947, 2 years after the war ended.
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.
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.
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"?