It's not. Octavian doesn't seem to have visited Caesar in Gaul. No reason to think Pompey was engaged to Octavian's sister. Nothing about Pullo and Vorenus is known after the Gallic wars (which is the time period the series takes place in). Pompey wasn't consul in 49. I don't know we know anything about Atia except the name.

Was Rome "highly sexualized"? I don't know if I would call it such, but they liked sex as much as anyone else. Octavian, as Augustus, tried to restrain some of that so it must have been some sort of an issue.

I'm not sure what you mean by "use of slaves". There were a lot of slaves, and they were used for all kinds of things. Cicero's secretary Tiro was a slave, for instance. He collected and curated at least one set of Cicero's letters and published them after Cicero's death, so he had a fair amount of personal agency it seems. There are also the proverbial salt mines.

Rome is a fantastic drama, and it does a lot of things right; for instance in Caesar's triumph they paint his face red (oddly they did not do that for Octavian's triumph). Some things are supposition; we have no idea how legions rotated soldiers out of the front line, if they did at all, and there's certainly no reason I know of to think they used whistles to signal those moves.

You might ask /u/xenophontheathenian about the representation of the collegia; he knows a lot more about that than I do, but I bet it is mostly fantasy.

Are there any specific incidents you're curious about?