When Rosie and JoJo are eating dinner, JoJo taunts his mother and pulls the dish of bread to himself and takes a slice. The dish moves back and forth to its original spot with no bread removed.
Jojo's eyebrow with the scar changes from the eyebrow being shaved around the scar to not shaved and also in between these extremes.
When in the woods with the rabbit, Jojo's cap position is not consistent.
When Jojo first goes into the hidden place in Inga's bedroom, he pulls a flashlight from his right pocket. However, in the previous shot (and when he first entered the house), the flashlight can be seen clipped to the back of his belt on the left-hand side.
The first time Elsa is seen in the attic her hair looks greasy, stringy, and unkempt. the second time she is seen, a few movie-seconds later, her hair looks clean, not stringy, and freshly brushed.
Throughout the film the Nazis refer to themselves as Nazis. This is historical incorrect as they would have referred to themselves as National Socialists, National Socialism being the name of Adolf Hitler's political and social ideology.
Sam Rockwell's character, Captain Klenzendorf, displays a ribbon on his uniform which represents being awarded an Iron Cross 2nd Class medal but he is wearing it through his tunic's 1st button when it was regulation to wear it through the 2nd button hole.
Jojo's book "Yoohoo Jude - Exposé über die Juden" is a strange amalgamation of German and English. Every word - except "Yoohoo" - is correct German, which makes "Yoohoo" stand out, because it would be pronounced "Yoho", if read as German word. Yet they pronounce it "yoohoo" (in English). The correct German form would be "Juhu" - which exists and sounds exactly like the English counterpart.
The "free Germany" sign Rosie is passing around is on a modern bumper sticker. This goof may well be intentional. The movie is loaded with modern references that are played for laughs (using The Beatles and David Bowie in the soundtrack and lines such as Fraulein Rahm saying "O... M... Gott" instead of saying OMG.)
Hitler keeps offering Jojo cigarettes. Actually, the real Hitler hated them: Not only did he strictly forbid his generals and staff to smoke in his presence, but also decreed the first successful anti-tobacco laws in history.
Fraulein Rahm claims to have had 15 children. Although this is exaggerated for comedic effect, there was what was called the "Lebensborn" program that was intended to breed racially pure children. Over half of the children that resulted from this program were born out of wedlock. So even though she was addressed as "Fraulein Rahm", she did not have to married to have children.
When Rosie wipes ashes from the fireplace on her face to give herself a "beard" and to pretend to be Jojo's father, she wipes her face fully but her lips seem to be spared of the ashes. This can seem to be an error, but note that she wipes her face with her back to the camera, so it is quite probable that she sucked in her lips as she was smearing her face, thus sparing them from the soot.
Towards the end, when the Hitler Youth are sent into battle, Jojo is standing dazed while the other boys rush into combat. However, the eagle on Jojo's uniform is now on his left side. The boys' knives are on their right side, and they are all throwing grenades with their left hands. The film in this scene has been reversed.
When Fräulein Rahm talks to Klenzendorf and Jojo about her uncle becoming a "massive drunk" after talking to a Jew, you can see the actor playing Jojo start to laugh as she slides over to them. He then goes back into character and continues the scene.
In an early scene, some Hitler Youth are running from left to right in the forest. However, one of them has a red armband on his right arm with the swastika reversed when the armband should be on the left arm. The film has been flipped for this to happen.
Rosie smears ashes on her face to simulate a beard. Moments later, she touches the white tablecloth with both hands yet it remains clean. Either she washed her hands between cuts or, more likely, the ashes/beard were applied by the makeup artist - Rosie's back is to the camera, so we never really see her smear the ashes.
Early on during the training exercise, Jojo and Hitler are running side by side when Jojo steals a grenade from Captain Klenzendorf. The other Hitler Youth seated on the ground move out of the way of Jojo as he runs through. They also move out of the way from Hitler. However, Hitler is supposed to be imaginary. The other kids should never have seen him so they had no reason to move.
As Jojo and Rosie are cycling together on the main road, "burnt-out" road markings can be seen.
"Atchoo" joke would not work in German as the German for the noise made by a sneeze is "Hatschi" which sounds nothing like the word for Jew.
In at least one released version of the film (as broadcast by the FX Channel), Thomasin McKenzie's name in the end titles is missing the "T", listing her in the cast as "Homasin McKenzie". (April 2024)
The first time an American soldier is seen waving a flag from a balcony, it is one with 50 stars instead of 48. (A common mistake in WW2 films.) The error is later rectified by showing an American in a Jeep waving a correct 48-star flag.
When Rosie Betzler brings Jojo to the Hitler Youth, there is a map hanging on the wall showing modern Germany instead of the Germany during the WW2-period; e.g., without Silesia or East Prussia.
The Soviet soldier who catches JoJo wandering around the city shouts to him, "Niemiec!" [phonetic transcript] in modern Russian, while during WW2, and long after, the term "Giermaniec!" [phonetic transcript] was used in common language.
At the end, the hand motions Jojo and Elsa use are more modern. Elsa's are similar to the hand motions Emma Stone uses in La La Land (2016) when she lip syncs "I Ran."
It has already been mentioned that Hitler would have never offered cigarettes to Jojo because he was strictly against smoking. One may argue that this character is not the real Hitler but the imaginary friend living in Jojo's head, so it's just normal that he's different from the real person. However, Hitler's antagonism to smoking was almost as well-known in Nazi Germany as his mustache, and an avid fan of his would have never imagined him offering cigarettes.
Captain Klenzendorf, despite his supposed German accent, mispronounces the word "Fräulein" in the common American "Fraulein" manner. Interestingly, the person he's referring to is indeed listed as "Fraulein" in the credits, which somewhat legitimizes his error in a most obscure way.
In the last fantasy sequence, Jojo imagines Hitler eating a massive meat dish in the shape of a unicorn's head. Hitler was known as a strict vegetarian, so Jojo would not have imagined that.
All the German characters speak almost all the time English instead of German, and most of the German characters, including Jojo, speak with British accents.