I'm gonna try to summarize the historical inaccuracies in the entire film.

As the film opens we see Caligula with his sister Drusilla, although it is said that Caligula had incestious relations with her sister we are missing through all the movie his two other sisters: Agrippina (Claudius's wife) and Julia Livilla.

According to Suetonius, Macro gained trust by letting his wife Ennia be the lover of Caligula. The depraved palace of Tiberius in Capri was written by Suetonius but apparently is an exaggeration of Tiberius habits, it seems more accurate that Tiberius left Rome for his safety after all that had happened when Sejanus (his right hand and head of the pretorian guard was and killed along with his followers and friends). Tiberius unlike the movie have more trust in Caligula than Gemellus, despites being his grandson, he believed like many others, that he was in fact son of Sejanus, considering his mother was having an affair with him (And she was forced to die by her own mother). Wether Tiberius was killed by Caligula is only a posibility, we don't know much about the circunmstances of the emperor's death. Caligula was in fact married 4 times with Junia Claudilla, Livia Orestilla,Lollia Paulina and finally Milonia Caesonia. Macro was not killed in the way he dies in the movie but he died on his way to Egypt. Gemellus was killed during the beginning of Caligula's reign. The divinity of the emperors was something given after their deaths like Augustus and Tiberius but Caligula make the senate to adore him as a living God, after all he was the grand son of Augustus. And finally, Caligula was at a series of games and her family was not at the time, they were killed at couple of hours later.