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Wow, the only problem I have from time to time is my Bluetooth losing connection. My phone gets at least 5 hours of use a day, one way or another. I have never had any of the problems the OP is talking about. It must be a defective phone.
 
This phone has been rock solid for me. I think I've dropped one call in the time I've had it and it was because I was in a basement with skeetchy service in the first place.

Everything works great. Reception is better than my 3G and I don't have any proximity sensor issues. The phone never lags, it's always silky smooth.

I'm not saying yours isn't having issues, but like others have said just restore it and see if it helps. Also, issues like not getting a voicemail for a while, or not showing missed calls can be provider issues. If the call never came through then your phone won't show missed calls. If the AT&T server took forever to process a voicemail, it'll take some time to show up at your end.

Before you do anything like getting a different brand phone, try the restore and if that fails, try an exchange.

If it still happens, get a new phone. There is nothing more frustrating than paying $$$$ for a phone that people can't reach you on.
 
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