Factual error: Burkhalter refers to Jesse Owens winning the gold medals in the Berlin Olympics, and that Hitler left the stadium every time Owens was to be presented a medal. Truth was, Hitler left the stadium when another black man won the day before, and didn't snub Owens at all. In fact, Hitler wasn't in attendance the days Owens won.
Factual error: In the rec hall where Klink is weightlifting, there is an advertisement poster for the Grindelwald region on the wall, which is in Switzerland. The German propaganda poured a lot of money into promoting the Reich's own recreational regions through the "Kraft durch Freude" program. With the war going badly, they especially wouldn't want a "Look how beautiful Switzerland is" poster in plain view of their troops every day.
Factual error: About 10 minutes into the show, Newkirk is using binoculars to watch Klink put the combination into his safe. He goes one direction for the first number, the opposite direction for the second number, then goes in the same direction for third number. Opposite for the fourth number. For the radial tumblers to set, it has to be alternating directions.
Factual error: In this episode, the running gag is that Schultz keeps flattening Col. Hogan's pumpernickel loaves. In reality, pumpernickel is a very compact bread that contains virtually no air at all and is impossible to flatten in this way. The shape is also wrong: pumpernickel is almost always baked in rectangular baking pans. To avoid confusion: the original, German pumpernickel is quite different from what's sometimes referred to as pumpernickel in England and America.