Solution 1:

Most likely a bug. A search of the Bethesda forums yields this thread, specifically:

Skyrim's game day cycle is NOT properly synchronized with the game's clock, with days changing at seemingly random times instead of 12:00 AM when it is supposed to. If this continues for extended periods, it can result in a seriously broken clock, which can have disastrous effects on the game's AI. Specifically, any packages that are tasked to be executed on a certain day will become broken because the game day is cycling at... say, two in the afternoon. The cause of this bug is currently unknown, but what is known is that it NEEDS to be fixed, as it IS game-breaking.

There have also been sporadic reports from PS3 users saying this has happened to them, too, though I cannot confirm it for them. If that is the case, the problem might be that the game day cycle is frame-timed (though I can't say for sure what the problem is)."

One poster thinks that it's a bug from the Fallout 3 engine (on which Skyrim is supposedly based):

This is a bug carried over from the FO3 engine (not sure whether it was in Oblivion).

It's not the calendar that's messing up, but the day of the week transition, the two of which seem to operate somewhat separately.

So I think you'll find that the calendar has been managing fine, but it's the day of the week that will get all out of whack, changing at strange hours of the day.

Maybe they'll actually fix it this time, but considering how long it's been lurking in the game engine, I'm not holding my breath."

Bonus round: a plea from a fellow frustrated gamer @rockpapershotgun.com to fix Skyrim already. Read the comments for some lovely puns!