My wife's iPhone 4 started saying there was no SIM soon after leaving the store on launch day. Popping the SIM in/out, rebooting, and airplane mode would all temporarily "fix" it, but it always came back. It was dropping calls like crazy. I tried everything to fix it and scoured message boards, only to find that she wasn't alone with this problem--yet nobody had a solution.

Unless someone else found an amazing fix that we didn't, I'd recommend anyone with this issue to make a Genius Bar appointment ASAP. Despite their being long sold out of the new iPhone, she walked out of the Apple Store with a replacement in hand (they had some set aside for hardware replacements).