How important are correct date and time settings on the Xbox 360?
Solution 1:
I don't believe you'll have any issues under normal circumstances. Sometimes save games are tagged with the date and time they were made, so it might be confusing if the date and time are constantly being reset. For instance, many games feature a "load latest save" function, which might be confused if the date and time are not properly set. Otherwise I'm not aware of many things that change due to date and time in the Xbox 360.
A few achievements in games are tied to the current date, the Calendar Man one in Arkham City and a few "play online on this day" achievements in games like Halo 3 (one of the Vidmaster Challenges) and Saint's Row 2 come to mind.
If you're signing into Xbox LIVE, the clock should be set automatically. In fact, Microsoft says that you won't be able to set the clock manually when you're signed in, period.