In the first lineup of arrested suspects, some time around May 1945, Rudolf Hess is included. Hess had already been in prison in England for most of the war and wasn't brought back to Germany until October.
There's no way a Douglas DC-3/C-47 can make a trans-Atlantic flight nonstop as is depicted when the American prosecution team leaves the U.S. for Germany.
During the sentencing Keitel is referred to as an admiral instead of a general. In 1937, Keitel was promoted to the rank of full general.
Justice Jackson is portrayed as initially failing in his cross-examination of Goring and emerging triumphant on the second day. In reality, the cross-examination was a disaster and severely damaged Jackson's reputation. This situation was recovered by Maxwell Fyfe.
The actual jail at the Palace of Justice had cells on both sides of the corridor. In the movie, they are all on one side.
On an external shot of the court building just before Alec Baldwin's character is told of the film footage of the concentration camps, there is clearly no set above the ground floor main entrance, unlike other external shots which suggests the building has height.
In an early scene, set in London (a London bus passes by), Jackson and Maxwell Fyfe are exiting the building where they had the meeting with the French and Soviet judges. Over the door can be seen the number of the building, "1440". No address in Central London has a four-figure number because the UK does not use the block-numbering system popular in the USA, but simply numbers buildings within each street, beginning at 1.
Jackson and Maxwell-Fyfe exit a building established to be in London, but the building number is 1440, a much higher number than any street address in central London.