Factual error: Numerous times throughout the series, there are palm trees seen in different shots. Stalag 13 was supposed to be just on the outskirts of Hammelburg. The only place anywhere near there that could support palms was the area around the Bodensee (Lake Constance), so therefore the palms seen are a big mistake.
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Plot hole: In the cinema, Hogan and his female underground contact avoid attention from a passing plain clothes policeman by kissing. This is wrong for three reasons. Firstly, 3rd Reich Germany wasn't so liberal that open kissing in the cinema would have passed as normal, it would probably rather have been viewed as libertine and offensive. Secondly, the scene takes place with a speech of Hitler as the background, which can hardly be viewed as romantic, and thirdly, this is even more true for the Gestapo, who was tasked with ratting out political dissent. To a Gestapo officer, ignoring the Führer's speech and kissing instead would make them stand out doubly.