Dawson Casting: Because the series takes place over nearly eighty years, this is both played straight and later inverted with many of the same characters. Just to name a few major examples:
Derek Jacobi, aged 38, played Claudius from the age of 19 to his death at 63.
Siān Phillips, aged 43, played Livia from the age of 34 to her death at 86.
George Baker, aged 45, played Tiberius from the age of 18 to his death at 77.
Margaret Tyzack, also aged 45, played Antonia from the age of 27 to her death at 73.
Some examples where this is purely played straight include John Hurt (aged 36) as Caligula from the age of 17 to his death at 28, Christopher Biggins (aged 28) as 17-year-old Nero, and Graham Seed (aged 26) as 13-year-old Britannicus.
Dyeing for Your Art: George Baker, who was in his early forties, went on a regime of diet and exercise so he could realistically play a young Tiberius. He managed to equal the weight he used to have when he was twenty-four. It sort of doubles as accidental Enforced Method Acting (does that even exist?) as his tiredness and exhaustion from working out so much and eating so little actually made it easier for him to play an often frustrated and bitter character prone to mood swings.
On early episodes, Jacobi put a stone in his shoe so he would limp realistically. Once he got used to it, he didn't need the stone any more.
Baker lost a lot of weight to play Tiberius, which also made it easier for him to realistically play the mood swings, as the amount of diet and exercise provoked a lot of that for him in Real Life.
Because of the alleged curse that'd already claimed some lives, Brian Blessed was a bit anxious. While they were shooting Augustus' dying scene, there was a blackout. By the time they did the take, he was terrified he would actually die on set, so the terror in his eyes is authentic.
The British chieftain Caractacus in the final episode is Richard DeVere!
Plagiarism: Not this work, but it turns out that Richard Condon plagiarized several passages from I, Claudius in The Manchurian Candidate. This went unnoticed until a few years after Condon died.
Throw It In: For Livia's dying scene, John Hurt suggested Caligula actually jumped in bed with her, as that would be more realistic for the character. They made the take, and he spontaneously kissed her full in the lips to emphasise the kind of degenerate person Caligula was (Livia was his great-grandmother).