As Bruno is waving goodbye to his friends near the beginning of the film, you can see some gates behind his friends. There were electronic motor actuators on these gates that would not have been around during the 1940s.
In the scene where mother is knitting while listening to the radio, the actress is knitting using the British method, holding the wool in the right hand and "throwing" it. No German mother knits the British way and would use the continental method, holding the wool in the left hand and "picking" the stitch.
(at around 47 mins) After Bruno visits Shmuel and throws the ball into the concentration camp, Bruno comes back to the house, and as he shuts the back door he is caught by his mum. Yet as the camera moves to his mum and back to Bruno, the back door is ajar again.
The "hero" sandwich that Bruno attempts to smuggle out for Schmuel appears to be about six inches long. When it is later discovered on the ground after having fallen out of Bruno's pocket it is several inches longer.
Near the end of the film Bruno and Shumel are led on a march with other Jewish inmates to the gas chambers by Sonderkommandos. In reality though Sonderkommandos despite having no choice but to work for the Nazis didn't help to kill the other Jews but instead helped to dispose of the dead after the Jews were gassed to death.
Apparently Bruno is allowed to do activities such as playing 'airplanes' and draughts (checkers), while until she is brainwashed Gretel plays with her dolls. In reality children in Nazi families were forbidden to have fun and instead focus on the 'Fatherland' and support the Third Reich. This explains why Herr Litz told Bruno he had to turn his mind to the 'real world' which was why Gretel decorated her room with Nazi posters and dressing up like a female solider.
"The story mixes up the German Wehrmacht (army) and the SS (Hitler's paramilitary "protective" forces). While the Wehrmacht was not directly involved in the holocaust (though they committed war crimes and killed civilians), the SS was in charge of the concentration camps. Bruno's father's uniform is a mix of Wehrmacht and SS. The Wehrmacht uniforms were green, whereas SS uniforms were black and had the skull ("Totenkopf") symbol on the cap." Incorrect: the black "allgemeine SS" uniform, so beloved of Hollywood because of its iconographic qualities, was discontinued during the war. On the green 1940-1945 SS uniforms, the black colour was only retained on the peaked cap bands, the collar patches, as underlay for badges and on some varieties of shoulder board pipings. Camp Guards wore copper-brown uniform piping, the "waffenfarbe", denoting the camp guards branch. Just look at the original pictures of uniformed SS guards in the camps from the period 1940-1945.
The dedication document shown at Bruno's grandmother's funeral is titled "von dem Führer" (by the Führer). It has been claimed even though the grammatically correct German would be "vom Führer", the text would still be too sparse and informal for such an occasion as a funeral. However, "Vom" is just a contraction of "von dem" but "vom" is more colloquial in German. An official piece of writing like shown in the movie would state "von dem", that is, if such a dedication is actually based on an original anyway.
"In the beginning of the film the main character's father has the common SS bullets on his right collar. Shortly after, the Father's uniform collar changes to a Skull and Crossbones patch, which is inaccurate. The Skull and Crossbones or "Totenkopf" was worn on the SS man's Hat." This is not a goof: the Totenkopf insignia was used as a "trade" badge on the collar patch by that branch of the SS that guarded and administrated the camps, the so-called "Totenkopf-Verbaende" that were part of the SS-Verfuegungstruppen". They wore this variant of collar patch in combination with copper brown piping, "waffenfarbe", denoting the camp guards branch. The SS hat badge consisted only of a skull, without crossbones. Just look at original pictures of uniformed SS concentration camp guards.
At the farewell party in Berlin at the beginning of the film, the singer with the dance band was using a Shure 55SH, an iconic American microphone. However the Germans would have used Sennheiser or Neumann microphones. They were very proud of their engineering, and pioneered early audio recording technology which is still sought after by collectors and studios.
The Kommandant (SS-Obersturmbannführer (Lt.-Col.) is wearing the "Blut-Orden" (Blood Order) on his right breast pocket which was awarded SS members who took part in the Munich Beer-Hall Putsch of 1923. However, on his right forearm he should also have the "alter Kämpfer (old fighter)" chevron, similar to a corporal's stripe, which was awarded to all SS members who served prior to 1933 - which as a veteran of the Putsch the Kommandant was supposed to wear.
The goof item below may give away important plot points.
At the end when Bruno is in the gas chamber and his family is getting to him to save him in time, the poison is poured down the chamber just before Bruno's dad arrives, and we learn it is too late. However, Zyklon B, the poison gas used in the chambers, took 10-20 minutes to kill everyone in the room.