Re: Incoming calls not ringing through and no notifications of missed calls
Most obvious thing, but have you rebooted the phone, and done a battery pull? If not, try that first.
If that doesn't resolve it, are you rooted / running a custom ROM, or have you frozen/disabled any apps? When calls don't ring through at all, do they go to voicemail, or do they not come through at all?
I've had calls go straight to VM occasionally, and think it's just carrier / tower glitch, but if it's happening to you frequently it may be something else.
In the phone app's settings, make sure Call rejection isn't on. In Settings, make sure Blocking mode isn't on..Go into Application manager, scroll right to the All tab, scroll down to the Phone app, and clear cache. If that doesn't do it, try clearing data.
Actually, as I reread your post, this could be a carrier issue. You say it's sporadic, and if it's happening to outgoing calls that doesn't seem likely to be your phone. I'd call you carrier and discuss the problems with them, too,
If all else fails, you can try a factory reset.