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: The rank badges on the SS Uniforms often do not match the character's spoken rank. For example, Maj. Hochsteter the regular Gestapo officer displays the rank of a SS Colonel (Standartenführer). His correct title would be Sturmführer. Also he is of lower rank than clink or Hogan and should be addressed as "sir" not the other way round, even if he is Gestapo. Hogan always calls Kink "sir" which again is wrong as they are both of equal rank.
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.
Factual error: Throughout the series, the SS and the Gestapo are often used interchangeably, as if the two organisations were basically the same. The most notorious example is "Major" Hochstetter, who sometimes claims to be Gestapo, sometimes SS, most of the time wearing an SS uniform. This is historically incorrect. The SS was a paramilitary and military organisation, while the Gestapo was a secret police force and since 1939 part of the Reichssicherheitshauptamt. The Gestapo, being essentially a plain clothes police, never had any uniform of their own.
Factual error: Towards the end of the episode, Burkhalter gets a call from a General Seidenbaum. Anybody with such a "Jewish" name would have been weeded out of the officer corps by the Nazis. In fact, anyone of that name would have had great trouble even getting his Ariernachweis (proof or aryan ancestry), and without carrying a copy with him he could not have opened a charge account at the local bakery. Most people with such names (those who managed to pass the Nazi board of racial review) had them changed to more "German" ones like Müller or Schmidt to escape the constant bullying. A little bit of background on "jewish" names: At some time during the medieval period, Jews in the German Reich who traditionally didn't use last names were forced to have them. Many selected names like Gruenbaum, Cornfield, etc. Which over time were perceived as "typical Jewish" names, even though many bearers weren't even of Jewish faith any more.
Factual error: In several episodes, German hand grenades, the famous "potato mashers" are seen. In (almost) all cases the Stielhandgranate 43, easily identified by its pull pin through the base of the head, was used. If the series is set in 42, the grenades should be the 24 or the 39 model, because the Stielhandgranate 43 - as the name suggests - was introduced in 1943 and didn't see widespread deployment until 1944. The earlier models didn't have a pull pin but used a pull cord that ran through the handle and was hidden by a screw cap at the end.