I've restarted once because something in Safari locked the whole phone. Some apps are broken (Podcasts), or look wonky in spots (Find My Friends). Everything mostly works, though. Even the Pebble app to connect to the Pebble watch. I figured if anything would break, it would be that.
If you want everything to work all of the time, never put the first iOS beta on your phone. Something is always not right. (Last year I was at WWDC, and the new maps app wouldn't render maps for me, just a grid. Not knowing SF that well, that was a major breaking change for me. <G>) Wait until beta 3 or so if you need reliability.
Have had a few issues with apps, most notably the Apple podcast app which is completely broken. Had one incident where the lock screen was totally blank other than the top bar but was fixed by a restart.
As for bugs and such, I haven't encountered any that would stop me from using the beta or are frustrating. The only app I have right now that crashes on my is Google+.
Don't forget that certain apps will not work. For example, neither the eBay app or MLB apps are working for me (and I use those everyday too).
I can deal with all the other issues, but terrible battery life is a dealbreaker. I'll hold off putting it on my primary phone until it improves.
Upside is it's nice having a break from my phone.
Pros ~ Two words - Control Center. I can easily change anything that I want without jailbreaking. It seems like they are moving towards an SBSettings-like iOS. For reference, SBSettings is a jailbreak-only package that allows you to change nearly every aspect of your iDevice.
Cons ~ Some apps are broken and will just not really work (ie. Alien Blue) with iOS 7 yet. Lag is very small but just enough to be noticeable. Restoring from a backup may take overnight, depending on the amount of data you already have. Some features can take some getting used to before you feel comfortable (ie. displaced 'delete' button when typing in passcode).