Factual error: The German agent pretending to be an American pilot is wearing a one piece flying suit from the 1960's when he is questioned by Hogan and the British escapee in the barracks. It even has the US Air Force logo on the sleeve, which didn't come into use until 1947, after the war.
Hogan Gives a Birthday Party - S2-E1
Factual error: When the crew in the plane gets ready to drop the bombs on the refinery, Hogan (in the pilot seat) tells Carter (who is looking through the bomb sight) exactly when to push the button. In fact, the pilot of a WW2 bomber had no way of even knowing when exactly to release the bombs - it was the job of the bombardier, looking through his targeting optics, to know that. Carter at the bomb sight should be telling Hogan how exactly to steer to get the bombs onto the target.
Praise the Fuhrer and Pass the Ammunition - S2-E19
Factual error: In the ammunition dump, a sign saying "Warnung Hoche Sprenggefahr" can be seen. That is not correct German. First, and foremost, it must be "hohe" and not "hoche", the latter form does not exist. Secondly, the word "Sprenggefahr", while not formally wrong, was never used in German. Depending on what the meaning of the sign is supposed to be, it must either be "Explosionsgefahr", if the overall danger of an explosion is meant, or if the property of the ammunition of being explosive is meant, it should be "Hochexplosiv." If the general presence of explosive material is being warned of, "Explosivstoffe" or "Hochexplosives Material" would be possible.
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.
Factual error: In this episode, the HofBrau (which should correctly be written "Hofbräu") is displaying a big red neon sign above its door. From 1939 on, air raid regulations throughout Germany strictly prohibited any unnecessary display of light at night. Any light visible from more than 500m away was considered a breach of air raid regulations.
The Great Brinksmeyer Robbery - S2-E18
Factual error: In the restaurant in Hammelburg, where Schultz discovers Hogan and Newkirk, there's an advertisement for "Brauerei der Jager, Stadt Wien." (Wien = Vienna) Vienna and Hammelburg are more than 500km apart, and if Hammelburg were near Düsseldorf, where the series puts it, it would be more like 700km. That's a bit far away for a brewery to advertise in the pre-globalisation era.
The Rise and Fall of Sergeant Schultz - S2-E6
Factual error: General Kamler awards Schultz what he calls "The Iron Cross Fourth Grade." There never was a version of the Iron cross called that. The Iron cross came in two ranks, called 2nd class ("zweiter Klasse") and 1st class ("erster Klasse"). The ranks higher than that were called the Knight's Cross ("Ritterkreuz des Eisernen Kreuzes") and were never pinned to the chest but worn around the neck.
Everyone Has a Brother-in-Law - S2-E23
Factual error: Schulz repeatedly calls Klink's adjutant "Kapitän." In the German armed forces the rank Kapitän only exists in the Navy, the German equivalent for the American rank of Captain (which is obviously meant here) is Hauptmann or Stabshauptmann.
Factual error: In the very end, Klink comes up to the boys. As he stands beside Hogan, the Desilu Studios Water Tower is present behind them.
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.