According to an Apple support document, the Do Not Disturb bug found this week will sort itself out Monday, January 7th.
Just uncovered by The Next Web, Apple acknowledges the problem and says it will sort itself out on January 7th. In the meantime, you need to remember to turn Do Not Disturb off manually:
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.
Via Apple Support.
The whole glitch, which Apple seems to have a knack for doing pretty often, has been made all the more ironic with the commercial airing this week featuring the Williams sisters and this very feature of iOS 6.
I suggest setting a repeating reminder to turn Do Not Disturb manually for the next few days until it sorts itself out. What I found odd was that yesterday DND turned itself off just fine. Today? Not so much.