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.