Apple has acknowledged its serious Do Not Disturb bug in a brief support article. The bug is supposed to resolve itself on Monday, January 7th, 2013.
The full document:
After January 1st, 2013, Do Not Disturb mode stays on past its scheduled end time.
Do Not Disturb scheduling feature will resume normal functionality after January 7, 2013. Before this date, you should manually turn the Do Not Disturb feature on or off.
To turn off the scheduling feature, tap Settings > Notifications > Do Not Disturb and switch Scheduled to Off.
For now, just manually turn Do Not Disturb on and off.