I believe that the problem is actually on the backup. Some database entry in the past has probably got screwed, but still ended up being backed up. I've had this once where some song wouldn't play properly or at all. Restoring from the backup just brought the problem back. The solution was to set the phone up as a completely new phone and then bring whatever apps and music i wanted back across. The disadvantage of doing this is that all text messages and phone logs were gone. Personally I could live with that as text messages for me are disposable communications and have little relevance once the message has been read.
If you're running windows or mac pre 10.9 then all your contacts and calendars will resync. If you're running Mac OS 10.9 then calendars and contacts will need to be resynced via iCloud, or if you don't use or want to use iCloud then you'll need to setup a caldav and carddav server in order to do this. Apple removed local sync services from 10.9. (utter madness)
I reckon you've basically got 2 choices here. Either live with the problem, or set the phone up as new on the understanding that you'll lose data such as text messages, progress with games, and certain in app purchases.