Given that finding the year is basically counting seasons since an arbitrary point, where there any times in which historical documents or accounts used the wrong date, either by error or local difference in calendar system? I can imagine outside of major cities there probably weren’t a lot of people per community who would actually receive value from keeping track of their calendar date?
I know this probably isn’t common, but I’m curious if it’s happened. I’m assuming most civilizations that wrote things down had calendars of some kind.
This is a very general question. Where errors were made, it’s difficult to say whether they were due to calendar calculation errors or something else. However, we have plenty of examples of this - in fact, ancient histories and king lists tend to be treated with extreme caution by modern historians. We have many examples of events, wars, kings’ reigns, etc. recorded by different sources as happening in not just different dates but different centuries, frankly often interspersed with blatant mythology. So the answer to your title question is: we don’t.
Usually in ancient history we don’t have some very clear exact date for some event and then look at the copious records. Instead, records are scant and usually our only information about an event happening will be from one or a couple of sources near the event.