Leifmk
Deity
Not having a year zero messes up calculations in astronomy and history.
It's not really a noteworthy problem, I think.
Astronomers already use a separate chronology, counting days from an epoch in prehistory... let me look that up... yeah, the Julian Date, which must in no way be confused with the Julian calendar. Their epoch is deliberately set before any historically recorded astronomical phenomenon, but does extend backwards into negative numbers (with the epoch itself being day 0).
And those historians who need to calculate the length of an interval of time spanning the BCE/CE era are pretty much all aware of the non-existence of a year 0, so I don't think it's much of a problem for them. (Inaccuracies in source materials are more bothersome.)
I suspect that the main effect of our common calendar not having a year 0 is a bunch of arguments between nerds on the intertubes.