But I don't want to fight!
I found an article that discussed the inaccuracies in I, Claudius. And both the Rome articles I've linked, praise the series while pointing out it's short comings. It was a joint US-BBC production, at least half a gold standard.
The key is taking into consideration what is being watched, especially when it involves dialog and reading between the lines, such as the role of Livia (I,Claudius).
Regarding Rome, this
Wiki articles says:
There are numerous inaccuracies in the series' representation of various historical events and personages. Co-creator Bruno Heller has said: "We try to balance between what people expect from previous portrayals and a naturalistic approach ... This series is much more about how the psychology of the characters affects history than simply following the history as we know it".[53] Series Historical Consultant Jonathan Stamp also notes that the show aims for "authenticity" rather than "accuracy".[5][54][55] The filmmakers stressed that they wanted to portray a more accurate picture of Rome, a gritty and realistic city as opposed to what they call the "Hollyrome" presentation that audiences are used to from other films, with "cleanliness and marble and togas that looked pressed."[56]
And this:
As others have mentioned, the atmosphere was probably very close. The broad sweep of historical events is also very accurate, with the exception of the huge compression of time between about 42 BCE and 31 BCE.
The question becomes how important are the inaccuracies to the telling and enjoyment of the story. I'd say that for Rome, the Cleopatra aspect is a serious blow to accuracy. The only real way you can judge this is watching it or just dismiss and criticize it based on your prejudices. Seriously, no hard feelings on my part, relax.... I'll let you have the last word if you insist.
Interesting distinction between 'accuracy' and 'authenticity'.
Actually, I have nothing against 'authenticity' - it can add hugely to the sense of textural verisimilitude in a story.
And, likewise, - while 'I, Claudius' is not, of course, history, it is an intelligent reading of how and why events occurred. The thing with 'I, Claudius' was that the sequence of events, the timelines, the characters, the basic facts - were not traduced. Everything happened when it was supposed to happen, and in the right order. Thus, it got the historical basis, the ones about which there is rarely much argument isn serious history, the what (what happened), the who (who did it or to whom was it done), the when, the where - they are not tampered with for the sake of storytelling, or entertainment.
However, the debate over interpretation - (- such as how nasty was Livia, how clueless or responsible was Augustus) - the old why and how stuff - can, of course, be subject to some criticism in I, Claudius.
My problem with much US historical drama is that they find the reality too complicated - or, that they think the audience will find the reality too complicated - and therefore take shortcuts, - with character, with time - conflating individuals, and compressing time - which actually make a nonsense of the real historical story.
Personally, even with the needs of entertainment in mind, I don't think this is necessary. The real story can be told in an engaging and interesting manner, one which will compel the attention of an audience. For example, Game of Thrones doesn't do this; it expects the audience to follow a complex story with a vast cast of characters.
So, if a TV series says 'this is how we think history should have happened', well, I will accept that as a stance that is far more intellectually preferable to one that attempts to pass off as history a series of short cuts that make the true story an awful lot harder to understand. We can have both 'authenticity', and a credible degree of 'accuracy'.