It's even stranger to hear them inflect latin words that hadn't been used, at least in the sense used, until the Medieval Latin Period starting about 800 years after the events in the show.

In view of "I, Claudius", it will be interesting to see how Livia is portrayed.

Grant, did you notice the part where Pullo replied to Atia, "Yes, mum"? :D

Yes, the Latin that most people pronounce nowdays is the Vulgate, derived from the Church version of the Middle Ages. I learned what was called Augustinian Latin, which my teacher explained was supposedly considered by scholars to be the way Latin actually sounded before the Church got ahold of it as their exclusive domain. Even today I am thrown when I hear the "ae" not pronounced as "eye". My Latin teacher was really fun, he was very tall and gangly with a crewcut and a bow tie. His name was Horace. One day before class I wrote a full chart of "Horatius" on the blackboard, using all forms and giving the English translation. He was speechless, said in his 25 years of teaching he had never seen anybody think of that before ;)