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.
Plot hole: The ages of the children on the show are really inconsistent. When the show starts in 50 BC, Octavian is around 12, Lucius is an infant and Vorena the Younger is at least 8 (given that she must have been concieved before Vorenus left for Gaul). Three years later Caesarion was born. When Simon Woods takes over the role of Octavian, Octavian is around 19, as stated on the show. Lucius should be seven but looks like he's four and Vorena should be fifteen but still looks eight. Episode 9 of season two takes place in 32 BC, 18 years after the first episode. Octavian might very well be 30, but Lucius (who would be 18) is around seven, Vorena (who would be 26) is a pre-teen and Caesarion (who would be 15) is around eight. Even if the events were moved up so that episode 9 is actually set earlier, the ages of the children still don't match when compared to how much the other characters have aged.
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: The eagle was the standard of each legion, not Caesar's personal standard as stated in the series, even by Caesar himself (to Brutus). Also, the Aquilifer (eagle bearer) was traditionally bareheaded - unlike the other standard bearers, he did not wear a bearskin or a helmet.