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: The "Blue Baron" tells the dancer that the Kaiser gave him a certain medal. In fact, the medal he points to (and the girl fondles) is a WW2 repeat badge to the Iron Cross first class, instituted in 1939 to denote presentations of the Iron Cross first class to personnel who had already received it in WW1. He may have received the original Iron Cross from the Kaiser, but by the time he had a chance to receive that repeat badge, the Kaiser was long through handing out medals.
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.
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: 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.
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.
Factual error: Hogan mentions a store that offers "thirty percent off on T-shirts." T-shirts were mostly unknown in Germany during the 3rd Reich, and didn't see widespread use before the 1960s. Before that, the traditional Unterhemd, known in America as tank top or wife beater, was worn almost exclusively.
Factual error: In several episodes, Hogan's men communicate by radio with a British submarine, and the dialog hints that the sub is submerged at the time. During the WWII era, submarines could not communicate by radio without surfacing first. In most episodes one might argue that the sub could be running shallow with a mast up, which would perhaps be within the technical possibilities of the era, but in this episode, the sub is talking to Hogan's men while under attack by a destroyer. This pretty much rules out running at periscope depth, because ramming was regularly-used tactic for killing subs that were in the process of diving or surfacing. To avoid confusion: Nowadays, subs can communicate while running several hundred feet deep by using VLF and ELF. However, these are definitely not capable of transmitting voice, but are text-only.
Factual error: Erica says she has a plane to take Klink and her to Argentina. The only transatlantic airplane in Germany at that time was the FW-200 Condor, whose military value would have made it hard to requisition even for an SS Gruppenführer (which would be the real rank a "General" would hold in the SS, different mistake), let alone for his wife. Plus, even the FW-200 could not have made it even to the Brazilian coast without a refueling stop somewhere along the African west coast, which would have been a problem, because Germany had no possessions there. Klink, being a Luftwaffe (Air Force) officer, should have at least been suspicious of that plan, even if he didn't know all the details off the top of his head.
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 Bodensee (Lake Konstanz), so therefore the palms seen are a big mistake.
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.