Factual error: Caesar was not murdered on the Senate floor, as depicted in the series. That was the conspirators' plan, but when they learned that Mark Anthony was coming to meet Caesar, they instead lured Caesar into the portico of Pompey's theatre and killed him there.
Factual error: At the beginning of this episode, Pompey and Cato talk about the battle against 'the Illyrian pirates'. There were no 'Illyrian pirates' in Pompey's days. Those pirates had already been wiped out during the Illyrian Wars of 229 and 219 BC. The pirates Pompey did fight were from Cilicia, in the south of present-day Turkey.
Factual error: Brutus proposes that Caesar be made imperator. The word imperator would come to mean emperor during the age of the Roman Empire, but it did not have that meaning during Caesar's time. Imperator was a military title which Caesar had been given long before the events in this episode. Even if the word is used with its current meaning it's an error, as Caesar never became an emperor. The word Brutus would have used is dictator.
Audio problem: In the scene where Mark Antony and his men are attacked by a mob on their way to the senate forum, Mark Antony says, "Rally to me" three times. The first time he says it, his lips do not move. The third time he says it, the movement of his lips do not match the words.