I have a brand new iPhone 4S, running 6.1.2, consistently crashing applications from core services like iMessage to Evernote and Tweetbot. Phone calls can be sent and received, but experience 1-3 second 'black outs' where I can't hear the conversation. These happen on approx 2-5 minute intervals. I've restarted, hard restarted (hold down buttons for 10 sec) and resynched to iTunes.
Useful context: iCloud configured Exchange email configured via Zenprise
I'm glad to do every rational troubleshooting step, I just don't know enough about logging to imagine where to start on this one.