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.
Caligula is stabbed many times by the guards, yet his robe shows no signs of damage.
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.
When Caligula and Tiberius are commenting on the intoxicated soldier, Tiberius is seen holding a chalice in his hands. In the next shot, he is no longer holding the chalice.
Caligula gives the "thumbs up" gesture several times to indicate his approval, however in Roman times this gesture indicated death. An Emperor would give the thumb up gesture to signal that a defeated gladiator should be condemned to death.
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.
Naevius Sutorius Macro committed suicide in 38 AD after his arrest, and would not have been executed as depicted.
Most of the penises seen in the movie would appear to be circumcised, which would be inaccurate as circumcision was not practiced in Rome. However on closer inspection, you can see that the penises are intact with the foreskin retracted.
When Proculus is suspended on ropes, there are modern stainless steel carabiners attaching the ropes to to his uniform.
Caligula squeezes a lemon over a captured slave. Lemons did not reach Europe until the 2nd century, at least 100 years after Caligula's death.
There is a huge map of Europe and the Mediterranean on the wall. It is a modern, extremely precise map, much more precise than available at the time.
Many naked women have dim but visible tan lines, mostly around their hip area. However, topless sunbathing was then a thing of the future.
Nerva is shown killing himself in the year 37 AD. However, he died circa 33 AD.
Several women, especially in orgy scenes, clearly had surgically augmented breasts. This medical procedure would not be possible for almost another 2000 years.