Spoiler details will follow. You may want to look away now. Or you could find out what happens by reading a history book.
As it stands, I reckon it's an incredibly clumsy dramatic device, symptomatic of the spreading abandonment of basic narrative coherence in a lot of American cinema and television. It's like Pearl Harbor, which can never make up its mind if it's From Here To Eternity, Tora! Tora! Tora! or Thirty Seconds Over Tokyo.
Next, on Today this morning 'historical consultant' Jonathan Stamp (who is actually a producer of historical documentaries) was talking about how the series was avoiding 'HollyRome'. This might be true in the way that the city is depicted, looking more like a mediaeval city such as you might see in Kingdom of Heaven than what has been seen before in movies about Rome. Which is fair enough - ancient Rome was probably much more like a mediaeval city than is often thought. But in plot structure and approach many elements have been lifted from previous renditions. As in de Mille's films, Rome is a symbol of excess (like the very silly bull's blood scene - I don't believe you can get so soaked simply from cutting a beast's throat). And as usual the audience is both critic and voyeur, censuring the excess whilst enjoying all the gratuitous nudity and sex going on (all heterosexual, I notice - no sign of Caesar's alleged more than familial liking for young Octavian). The characterization of Atia is lifted straight from I, Claudius; like Graves' Livia Atia is manoeuvering to make her son most powerful man in Rome. And I doubt the real Atia was quite so ready to hurl off her kit and grab the nearest erection. Meanwhile, her son Octavian appears to have been cast for his resemblance to the young Roddy McDowell, in what seems a deliberate reference to the 1963 Cleopatra.
And then there's the comedy references. Some of the humour, like the troops waiting while Antony has a shag behind a tree, is deliberate. But sometimes comedy is unconsciously echoed. As Vercingetorix laid down his arms at Caesar's feet, I couldn't help but think of the same scene at the beginning of Asterix the Gaul. The opening titles, innovative though they are, remind me of the end titles of A Funny Thing Happened On The Way To The Forum, and I can't help but feel that it would look better to the theme from Up Pompeii. And I'm sure you can guess what I was thinking as they nailed Gauls to bits of wood. ("Crucifixion's a doddle!") I also laughed at the dormouse, but this was because of Mary Beard's mention of the 'dormouse test', a measure of the subtlety of a reconstruction of Rome by how long it takes anyone to be offered a dormouse, in Saturday's Guardian (I won't link to the piece, as it requires registration).
I don't want to be picky about details, like Caesar's laurel wreath, which he began wearing to hide his baldness, on a decidedly non-bald Ciaran Hinds, or the fictional first marriage of Octavian's sister. And I had fun watching it, and will watch more episodes. But in the end this is a made up piece of nonsensical fluff, that tries to impress the audience through scale (note how much of the publicity quotes statistics - 4,000 pieces of wardrobe, 750 extras, biggest set ever, etc., etc.). It's nothing more than this, and isn't half as important as it thinks it is.
* Yes, I know he ought to be Octavius at this point, but such a nitpicking name change would just confuse the audience.