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.
