At the moment it seems that UTC timezone is used for all calculations that involve "days" (Mortarboard, Epic, Legendary and other reputation/comment/question organization). I totally understand this from and ease-of-development perspective, but it seems pretty unfair to those poor users in the far-flung reaches of the US west coast (etc) because by the time you wake up the day is already almost half gone, and those of us with jobs can hardly be expected to spend all our time in the office on SO. I'd be curious to see a breakdown of these badges/user/timezone.
This issue has been raised before (where it was well received but declined) and Jon Skeet wrote an answer to a similar question essentially saying it would be a pain and would be subject to abuse (easy for him to say, as he's in the UK AND gets 200 points a second). However, recent changes to settings that limit the frequency with which you can change your timezone gets around the abuse issues, and I just can't imagine that the bright folks at Stack Exchange couldn't figure this one out. Hell, just create a setting what says "What UTC time would you like your 24 hour cycle to begin?"... any changes to this setting could be set to only take effect the following day, allowing no points-per-time-based badges in the intervening interval, or if that's too hard, just force uses to pay a point penalty to change this setting.
Whatever the mechanism, it seems like an obvious issue that should be addressed.