Audio problem: After Hogan and company get into the car to go to town to get Lebeau, Klink is walking around to get in the passenger side, Schultz takes off, leaving Klink standing alone. After Klink calls out, you hear the screeching of tires sliding on pavement. Trouble is, the camp doesn't have any pavement.
Plot hole: The prisoners fake a fire with some smoke bombs to have an excuse to rush into the print shop and smash up the print plates. Afterwards they even receive thanks and a reward for their valiant efforts. In reality, the guards would notice immediately that nothing in that room is even singed, but everything important has been smashed by fire axes.
Factual error: Erica says she has a plane to take Klink and her to Argentina. The only transatlantic airplane in Germany at that time was the FW-200 Condor, whose military value would have made it hard to requisition even for an SS Gruppenführer (which would be the real rank a "General" would hold in the SS, different mistake), let alone for his wife. Plus, even the FW-200 could not have made it even to the Brazilian coast without a refueling stop somewhere along the African west coast, which would have been a problem, because Germany had no possessions there. Klink, being a Luftwaffe (Air Force) officer, should have at least been suspicious of that plan, even if he didn't know all the details off the top of his head.
Continuity mistake: Carter and Newkirk have just taken the escapees down the tree trunk to the tunnels. When they go to open it, they clear off the snow to open it. When the shot goes to a German soldier that was chasing them, the phony stump is suddenly covered over again. It would still have been visible, having just been exposed.
Plot hole: When the driver of the car addresses Roberts (the real Roberts that is, not the double), Roberts reprimands him, telling him not to call him Baumann. It is safe to assume the guard was supposed to be speaking German, since he addressed Roberts by his German identity. That poses some interesting questions. Did Roberts speak English? In those days, most Germans did not even have a basic knowledge of the English language. Did he speak German? That would imply he has a good enough command of the German language to pass as a German. Roberts however isn't a spy like Hogan and his crew, but a pilot in the RAF.
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.
Continuity mistake: Hogan pulls a container with a red cross out of the drop box and opens it. It is labeled "penicillin" inside and contains among others several vials of clear liquid. Back in the camp, Hogan gives a box with a red cross on top to Kinchloe, saying "here's the penicillin." It is a completely different box.