After doing a Wikipedia dive and reading this /r/AskHistorians post: Has the current year format as we currently know it been followed for 2014 years?, my original question of "How confident in the 'Anno Domini' part of 2020 A.D. are we?" is still relatively unclear.

Unsurprisingly, it seems like it's pretty arbitrary (all the more reason those 1999 vs. 2000 pedants should shut up), but I still would like to know where Dionysius got that his current year was 525 A.D., and how accurate the Roman calendar system of "Xth year in the reign of Consul X" (specifically relating to Jesus' birth and death).

EDIT: This popular calendar post also fails to explain where Dionysius got 525 A.D. and why we now hypothesize he was off by about 4-7 years.