Charea proclaims Claudius emperor after killing Caligula and his family. In reality, it was another Praetorian who proclaimed Claudius as emperor; Charea had been planning to kill Claudius as well to eliminate the entire imperial family.
The credits say "Cast in Order of Appearence," but due to the heavy editing after the "director's cut", they are completely wrong in subsequent versions. Some characters credited in the beginning appear around the end, and vice versa. For example, Proculus is introduced early in the film, yet he is the last billed.
When Tiberius and Caligula are in the three-story sex building (noted by the man with stilts), first Caligula goes down, following Tiberius on the elevator. Later, they are talking at the bottom, then back on top of the building, then back at the bottom.