Corrected entry: It is made out in Series 2 as if Livia is Octavian's first wife. In fact she was his third wife. In reality his marriages to his two previous wives only lasted 2 years in total so historically they were much less relevant than Livia, the mother of Tiberius, the next Emperor.
Corrected entry: At the time the series is set the height of the average Roman foot soldier is estimated by historians to be about 5 feet 4 inches. A big chap like Pullo would have looked like he was surrounded by Hobbits in battle. The Celtic peoples that the Romans fought tended to be significantly taller due to a better diet than Mediterranean people. The small battle shown in the first episode is therefore not strictly accurate. As more Central and Northern Europeans were recruited by the Romans the average height of the army rose. Excess character height tends to be a mistake in all historical dramas and would be extremely difficult for the directors to correct.
Correction: When real people are portrayed in films, the actor or actress is often the wrong height, as acting ability generally takes precedence over exact appearance. Likewise many other physical factors (age, hair colour, weight) take second place to the quality of the performance when casting. In a nutshell, using actors of the wrong physical appearance is completely standard in films. As such, in common with other standard movie conventions, this sort of thing is not considered to be a mistake.
Corrected entry: Atia of the Julii was in real life a religious and caring woman, considered by historian Tacitus to be the ideal Roman matron. She was definitely not a cheap trollop as depicted in the series.
Correction: The filmmakers do not claim to be historically accurate.
Correction: Creative license. The show also leaves out Brutus' wife, several of Antony's wives and Octavia's husbands, along with a number of children. They have to leave some people out, or the show would have too many characters to focus on. Furthermore, while it is IMPLIED that Livia is his first wife, it's never actually STATED. He could have been married before when he was living with Agrippa.