I am using an iPhone 4s with iOS 6.1.3
I have "Do Not Disturbe" scheduled to turn on in the evenings and turn off in the mornings. It appears to be working correctly, as the half moon icon appears and disappears as per the scheduled.
I have set the settings to allow "Favorites" to bypass the "Do Not Disturbe" setting and I have eight family members noted as "Favorites."
The problem: When the "Do Not Disturbe" setting comes on as per the schedule, in coming calls from my Favorites do NOT bypass the "Do Not Disturb" setting.