SAME ISSUES, iPhone 4 sent back for replacement...
I have the same issue, Started yesterday. When I first got the iPhone 4, iTune says "No SIM installed". I figured it was just some initialization problem, unplug and plug the SIM back in, that fixed the problem and iTune was able to recognize the SIM and I was able to do the activation.
However, the "No SIM installed" problem appeared through out the day, every time the problem is solved either by take out and put the SIM back in or putting the phone in flight mode and back to normal mode. Eventually Apple suggested going down to ATT and get a new SIM to see if that solves the problem. So I got the new SIM card from ATT at about 6 p.m. when I wake up the next morning around 8 a.m. the phone was showing "No SIM installed" again. (I have also reinstalled the firmware at this point)
Call Apple back, kept on telling me it's ATT's problem. I told them no way, I told them that I can understand if the phone is telling me that is has "no service" then I can agree that's an ATT problem. But when the phone doesn't even detect the SIM card (the new one), I have to assume there is some problem with the phone. So eventually I argued my way through and ask them to take it back for repair or a replacement. They said they will have to look at it and decide if this is a phone related problem and not something to do with ATT...
So after less then 48 hours and about 5 hours on the phone with the Apple advisor. I now have no phone, and I'm having hard time finding a phone to use because I'm now left with a micro-SIM...
Good one Apple, just keep blaming on ATT!!!