Mistakes
There are a few mistakes in the movie (Some are logical bloopers: something just doesn't make sense. Some are historical mistakes.)
1. In the movie, Goring is cross-examined by Jackson before the Christmas Eve. In fact, the trial began on 20th November 1945 and cross-examinations began on 18 March 1946. The trial ended on 1 October 1946 so Goring couldn't make his testimony before Christmas Eve.
2. In the movie, Keitel's last words are: "I'll join my sons. Deutschland uber alles!". In fact he said: "I'll ask the Lord for mercy for the German nation. Alles fur Deutschland!" (When you quote somebody's last words it is IMHO polite to quote them good even when he was a criminal.)
3. When the prisoners arrive at Bad Mondorf, Julius Streicher names Dr Robert Ley (the one who strangled himself before the trial began) "Drunkard!" (with hate in his voice). In fact Dr Ley had only one real friend among the defendants and it was... Julius Streicher. (Goring could have said that. After Ley's suicide, Reichsmarshall said: 'He would die anyway, having nothing to drink except for water.')
4. Logical error: Field Marshall Wilhelm Keitel is mistitled as "Admiral" at the final statement.
5. The circumstances of Goring's surrender were quite different that those stated in the movie. (There is also discrepancy on the dates: various sources state that he surrendered on 2 May, some others say 6 May or 9 May.)
6. The scene where the verdicts against all defendants are handed down. In the movie, defendants are informed if they were found guilty or not and their verdicts are handed down to them at the same time. In fact, on the final day of the trial on 1 October 1946, there were two session: the morning one, where all defendants were informed if they had been found guilty or not, and the final afternoon session on 2.50pm, where the verdicts were handed down. The first session was regular, with all defentants present, but the second was different: every defendant was brought in the courtroom alone, and so he was informed about his verdict. The light was dim and no cameramen or photographers were allowed to be present at the courtroom at that moment.
7. The execution was witnessed by fourteen people: Colonel Burton Andrus, four generals (British, French, Russian and American), eight selected journalists and German, Dr Wilhelm Hoegner (who soon became Prime Minister of Bayern), who acted as "The Witness Of The German Nation". There is one thing I am uninformed about: were the journalists allowed to take any photos during the execution? The dead bodies were later photographed by military photographer, dressed and naked, and were meant to be "CLASSIFIED" but somehow some newspapers published them soon afterwards.
8. Logical error: the execution scene. Ribbentrop, Keitel and Kaltenbrunner are hanged, Col. Andrus goes for the next man and mutters "Three.". Next, FIVE men are hanged, but when Andrus goes for the next one, he mutters "Seven." (The order in which they were executed also differs lighlty from that presented in the movie.)
9. Small thing: the movie is concentrated on Goring, Jackson and partially Speer, and some other defendants are minimized. We are not informed by the movie why Rudolf Hess in the final scenes acts like madman (the case of Rudolf Hess deserves a different post, it's very strange and curious), or why Streicher or Rosenberg were sentenced to death. The movie completely omits Wilhelm Frick, who was terrible figure and fully deserved death sentence, and Arthur Seyss-Inquart, who did in occupied Netherlands exactly the same that Frank did in Poland - mass executions, Jews' extermination, deportations etc. It is also not stated why Hans Fritzsche, Franz von Papen and Hjalmar Schacht were freed (in fact no one of them deserved to be sentenced). This hurts the movie a bit.
10. The concentration camp footage is named by Jackson's assistant as made by Allies after the liberation of the camps. The footage presented is a compilation of movies actually made by Allies and some movies made by SS figures for private exhibition (torture scenes, bulldozer scene).
If I find something more, I'll let you know.
Thank you for your attention.