Factual error: In many places throughout the series, the characters transmit real names or other identifiable personal traits over the radio. In S5E12 for example, LeBeau asks for and gets the name and phone number of the female Resistance member he is talking to. For her sake we can just hope the German signal intelligence corps was sleeping on both ears that night, if not the Gestapo could find her with nothing more than a phone book. For the younger ones among us: Today radio links are digital and encrypted. Back then, voice communication over the radio was pretty much "in clear" unless you transmitted only code words.
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: 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. 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.
Factual error: Throughout the show, German officers talk about "Nazi" this, "Nazi" that, even in official capacity. In fact, the mere mention of the diminutive "Nazi" could get you in serious hot water for the disrespect and dissent it implied. Correct would be either "National Socialist" or some reference to the Reich: e.g. "Officer of the Third Reich" instead of "Nazi officer."
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.
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.
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: When the farmer sticks his turning fork into the haystack, a scream is heard, but then everybody emerges unscathed. Wounds from turning forks aren't like sitting on a brass tack - even a quick jab usually earns you a trip to the surgeon (I've seen such wounds), a vigorous stab like the one in the scene would go through limbs and could easily kill a man. There's no way anybody would walk away from such a hit.
Factual error: Klink usually wears an EK1 (EK= Eisernes Kreuz = Iron Cross first/second class) chest cross with a WW1 EK1 repeat badge, but he neither wears an EK2 ribbon nor a WW1 EK2 repeat badge. This is not a legal combination, he either has to wear both or none at all. The EK1 and EK2 repeat badges were awarded to soldiers who were awarded an EK1 in WW1 and another in WW2. To be awarded an EK1, you had to have the EK2 already. The Legal combinations would be: EK2 ribbon in the button hole with or without EK1 chest cross, EK2 ribbon in the button hole with repeat badge with or without EK1 chest cross, again with or without repeat badge. One legal way of wearing it is seen in S5E3, "The Klink Commandos", where Hogan wears a black-and-white WW1 EK2 ribbon with repeat badge and an EK1 chest cross with repeat badge. It doesn't make any sense for him to wear that (separate mistake), but the way of wearing it is correct.
Factual error: During the show, many (not to say most) higher officers are seen wearing a Knight's Cross with Crossed Swords and Oak Leaves, the fourth highest award for military valor of the Third Reich. In fact, a total of 177 of this and higher-ranking medals were awarded during the entire war, most of them in '43 and after. The series is allegedly set mostly in '42. Historically correct, most Knight's crosses should be of base rank or with oak leaves only, as of these categories more than 8000 were presented.
Factual error: In many episodes, SS members of all ranks appear - the most notorious recurring character being Major Hochstetter. Curiously enough, Hochstetter couldn't have been a Major in the SS, simply because that rank didn't exist there. The SS used the SA rank system, not the Wehrmacht one. Hochstetter for example would have to be a Sturmbannführer. Colonel Feldkamp would have to be a Standartenführer. To avoid confusion: Hochstetter sometimes claims he is Gestapo, even when he's wearing an SS uniform (different mistake). However, he couldn't be a major there either - he'd have to be a Kriminalrat or Kriminaldirektor, because the Gestapo, which was in principle a civilian police organisation and wasn't half as closely integrated with the SS or the military as the series would have us believe, didn't use military ranks at all.
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.
Factual error: All through this episode, characters keep referring to the river the bridge *du jour* spans as "The Düsseldorf" or "Düsseldorf river." The city of Düsseldorf is situated on the river Rhine - there is no "Düsseldorf river." It's a well known fact that the producers were hardly geography whizzes, but not knowing the Rhine is bad even by their standards.