This has been going on for a while now - I've heard a couple of different explanations as to why:
-there is a tower out of service in Destin, which is being replaced
-AT&T is bringing 3G to our area, and the changeover is causing issues
-the new software update has a bug in it
I have no idea if any of these are true, but I know that everyone I know with an iphone in the area is having problems. I have been getting delayed calls and voice mails, and sometimes texts - any missed calls don't show up until I make a call, and the voice mails and texts sometimes take days to show up. If I try to listen to a voice mail by just hitting "play", nothing happens; I have to call myself and push * when my greeting comes on to hear any messages.
My problems seemed to start earlier than some people (this has been going on for 2 months for me), and maybe they are resolving sooner too (again, I have no idea why this is...) As of the past few days, I am now getting all my calls and texts immediately, and voice mails show up (visually) immediately too, although I still have to call in manually to listen to them.
Despite the problems in service, I still love my iphone. Keep bugging AT&T, sooner or later they will fix it completely.