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: The future emperor Augustus is called Octavian, an English modification of Octavianus. However, before being adopted by Caesar (which happened after Caesar returned from Egypt) his name was Octavius. When he was adopted he took the name Gaius Julius Caesar Octavianus, and at that point the English version of his name is Octavian, but before the adoption he did not have that name. On the show they are thus calling him by a name he did not have at the time.
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.
Factual error: Cicero's secretary, Tiro, is seen throughout the series wearing a plaque around his neck marking him as a slave, and in episode 2-6, Cicero tells him, "You've been freed in my will". However, Tiro was freed in 53 BC, several years before the events depicted in the series.