Dating systems: BC and AD, or BCE and CE?

[M. Caecilius]

I'm not so sure about that. The fact that a major genre of Roman historical writing were the "Annales" suggests that the years were very important, even if dated by the consuls rather than by what we would, in the modern world, consider a sensible, sequential system. The sequential system was just more complicated.

The Libri Pontificales and the Annales Maximi may have dealt to a large extent with political and religious matters, but the fact that they were kept in the year-by-year fashion, the Roman legal concept of precedent, and some of their antiquarian research (whence the concept of A.U.C., I believe) also make it appear to me at least that dates were important.

I have no idea how any reader of, say, Livy was expected to remember quite when some obscure personality in the early days of the Republic was supposed to have been consul, but the lists were likely available (and sequential) and the upper class at least may have learned large swathes by heart; although tombstones of the ancient world hardly ever give a proper date, they tend to record to the day how old the deceased was, indicating that some kind of records and ideas of sequence existed.

As regards the Greeks, the Olympiads were not quite as exact as Years, but they were sequential, and used whenever it was thought important that someone from Thebes and someone from Syracuse were on the same page when reading a work composed in Athens...

Lack of accuracy is a problem, of course, but not necessarily because it was not a concern.