BJ has consistently been identified as a US Army Ranger, however, in this game he wears the patch of the 101st Airborne. He late identifies himself as a Ranger upon awakening from his coma, which would mean he was part of the Ranger Regiment since Ranger School was not founded until 1950. It is not known why he is wearing the patch of the Screaming Eagles.
When Fredrich Keller was captured by B.J., he was seen in the garage strapped to the chair he was in, but he was able to get up and stab B.J. with a screwdriver. But when the next scene comes in, Keller is again strapped to the chair.
Klaus Kreutz, who's a former Nazi soldier, is seen with tattoos. In reality, Nazi Germany had a strict rule against their soldiers having a significantly huge amounts of body art. Klaus' tattoos would be too big for the Nazi military regulations.
During the game, there are a good number of cigarette ads on the walls in some stages. The character Bubi is also seen smoking on the Berlin train in one of the stages. Nazi Germany was one of the first countries in recent history to discourage smoking among it's citizens by banning it in public places (such as trains) and on-duty military officers were restricted from smoking.
When BJ and Fergus meet Wyatt, he identifies himself as being part of the "109th Airborne." However, all American Soldiers in the prologue are wearing the unit patch of the 101st Airborne. The discrepancy is never explained.
Fergus Reid is depicted as a pilot for the Royal Air Force (RAF), but he conspicuously wears patches from the British Parachute Regiment, including the rank of sergeant, which is actually a part of the Royal Military, not the RAF.
B.J. stated that he's in the US Army Rangers. That would mean that he would conduct missions and assaults from the ground, not from the air like in the game.
In the Nazi Lunar Base's War Room, you can see a screen which depicts the world with the "current" national boundaries of the real world. The story of the game is in an alternate timeline, so the boundaries of the world should be notably different.
When you bring Max Hass his missing toys, he is sleeping. If you look at his face, his eyes are still open.
When Set takes control of a robot, he uses it to grab and pick up Frau Engel by her face causing damage. When Frau Engel stands up and looks directly at Blazkowicz, her bottom jaw is dislocated and most of her lips have been torn off, making talking impossible. But, when she threatens Blazkowicz, she is speaking in completely coherent sentences.
The game depicts computer terminals with built-in displays, some of which didn't exist until the late '70s and early '80s. Given that the game takes place in 1960, we may assume possibly that the Germans, having won the war, with Deathshead's help are a bit more advanced, hence the Lunar base, etc., but this still seems too much given the other heavy computer machinery is appropriate for the '50s and '60s rather than showing vacuum column tape drives which would have been released in between PCs and the '60s.
In the first stage of the game (which takes place in 1946), the Allies were using B-17 bombers, even though the B-17 was officially replaced by the B-29 two years earlier.