Caesar had himself made Pontifex Maximus (chief priest) so he could reform the calendar, which he did while still alive in 46-45 BC. So at the time he died, the Romans were using his calendar.
From what I’ve read, they actually messed up the leap year thing at first, having one every 3 years instead of every 4. This was fixed by Augustus who dropped some leap years to get the calendar back on track. Here’s a good article from the BBC about it:
Here is something from the Times, March 15, 1956:
“Is today or isn’t today the 2,000th anniversary of the death of Julius Caesar? That is the question among classical scholars. Some hold it is the 1,999th anniversary.”
FWIW, March 15, 1956 was a Thursday and if it was really the 2000th anniversary, the original date would also have been Yom 5 (=Thursday) in the Hebrew calendar. If that was only the 1999th anniversary, then the correct answer is Friday. That is likely the best that classical scholars can do.
I do believe that the Hebrew day count is exact. The uncertainty is what constituted 44 BC.
There being no zero year, I think the 1999th anniversary people were correct. Well sort of, see below.
The Ides of March that he died on was on the Julian calendar and we use the Gregorian. The Gregorian adjustment got the calendar to be in sync with the Julian as of the 3rd century AD. Caesar died a few centuries earlier, and the Gregorian calendar would have skipped 2 leap days during that time. So the 2000th anniversary of Julius Caesar’s death was 13 Mar 1957.
That would have been a Wednesday. The point is that if you knew the real 2000th anniversary then whatever day of the week that was would be the answer.