Factual error: When the SS guard is calling Sergeant Shultz after seeing the burning fuse, he addresses Shultz as "Sergeant", rather than the proper German word for Shultz's rank, "Feldwebel."
Continuity mistake: Hogan dumps a bucket of water on Barnes and Davis each, to make it look like they were the ones who hid in the tanker. They get big wet patches on their uniforms from it, but aren't completely wet through and through - which is to be expected, after all it's just a small bucket of water each. After the next cut however, they are completely soaked like they went swimming.
Revealing mistake: When the "Boat" is loaded on a "trailer", you can see that it has very little ground clearance. The wheels of the "trailer" actually are hidden behind the boards like on a parade wagon. The boat has no keel and no hull below its freeboard. Besides the question of how the boat got onto the trailer if it is practically built around it, there remains the question of how it is supposed to stay afloat without a keel or a bottom.
Factual error: The guard outside Klink's office and the two Gestapo soldiers guarding the gold truck have MP38/40 and a Thompson submachine gun, but carry rifle ammunition pouches instead of the long ammo pouches that carried the 30-round magazines used by the MP38/40.
Visible crew/equipment: Toward the end of the episode, after the two women are taken out by the Gestapo, Shultz, Hogan, Lebeau, and Newkirk are standing having a drink. The camera goes in for a close-up on Shultz, there is a noticeable shadow of the camera on Shultz's coat, and right arm.
Character mistake: When Klink explains the route of the trucks carrying the red cross packages to Kühn, he for once uses a map actually showing Germany. Unfortunately, the places he points to start near Luxemburg and track all across Germany. The spot he places Hammelburg at would be near Poznan in Poland.
Factual error: The American women the SS brings into camp claim to be entertainers having performed for troops. The series is allegedly set in 1942. Before June 6th, 1944 there were no allied troop concentrations in central Europe, certainly not in Germany, and very certainly none of a size and security rating the USO (or probably rather its predecessor organization, since the USO was founded in 1941 and would not have been fully operational yet) would send a troupe of female entertainers to.
Character mistake: When ordering Schultz to finish cleaning his car, Klink salutes Schultz, his returning the salute with the garden hose in his hand leads to Klink being soaked. A salute is, except in rare circumstances, always initiated by the lower-ranking individual and returned by his superior, not the other way round. This rule is broken especially by Klink in several other places as well.
Other mistake: Carter is washing things in front of the barracks. There is snow on the ground and on the windowsills and they are wearing winter jackets but the cold weather doesn't bother him putting his hands in the water over and over. He even gets splashed in the face but it doesn't faze him.
Plot hole: This episode revolves around training the reluctant, untalented Schultz to impersonate Klink to get the captured heroes back from the Gestapo. This is actually a pretty common theme, somebody, usually one of the heroes, impersonating an officer to free a prisoner. The plot gives no reason why this time, they would have to use the cowardly, untalented Schultz instead of doing it themselves.