Does it stick fairly close to history?

Octavia must have been very strong and may be she really loved Antony? She didn't remarry after his death and took care of his children, by Fulvia and Cleopatra. As Octavian's sister she must have been a very valuable piece of "marriage meat" for her brother. Despite his autocratic nature she kept independence. Probably, one reason was, that she bore 5 children. The women who bore 4- if I'm correct - due to imperial laws got a higher status - didn't need to have any "patron" who would take care of them.
Fulvia obviously wasn't in the series. Her story would need another series. Imagine a woman who declares a war against Octavius Caesar! For me she was the most fascinating of all Roman women and with her courage, impudence and image of her created by historians she must have been more interesting than Cleopatra. Atia's character is probably based a little bit on her, but J. Stamp said, her role model was Clodia, acually Fulvia's sister-in-law.
Cicero is as much "deified" as much Antony is "brutalized". I haven't read the books by Harris, but considering the sources Cicero was a bit of a cold bastard, vindictive egocentric and pompous instigator. Despite all that in his letters he appears as a very fragile manic-depressive. He was obsessed with the state matters, he was a very good questor and procolnsul and acted in just cases. On the other hand, he was a criminal defender, and supposedly having relationship with his own daughter, beloved Tulliola, accused of by Sallust (his wife Terentia second husband).
Strangely, even historians do not like to refer to that speculations, but they are very willing to mention all Antony's little sins. The same, Octavian's peadophilia acknowledged by many historians, as we should call the relations with little girls today. Comparing to all the above, Antony was only a big spender, always short of money, alcoholic with a great ego and the will of life.
And may be too naive and to sincere, as he was outmaneuvered by his friends, both Caesars incuded and Cleopatra.
As far as the plots omitted , there is all "Cleopatra story", after Filippi, and later, after Antony left Octavia. Worth to mention, someone killed Arsinoe, Cleopatra little sister, in the Artemis temple in Ephesus. Supposedly, it was Antony who ordered this. That would be a total nonens for him, as in this time he tried to regain the power in Asia province, and this event caused a serious riots in the city. And so on, and so on... So many things to say.

The episode with Livia is called "Necessary fiction" if I recall, so everything should be clear. Octavian was married even twice before Livia, his first wife was Clodia Pulchra, Anthony's step-daughter. Consequently, Antony had three wives before Octavia. All these persons, if included, would need a story as long and complicated as, let's say, GOT. I would love it, but probably the producers had some reasons to make it shorter.

Off course they are. I was just ironically admiring that they didn't go there... his expression was enough.