Seems to be a widespread problem, from what I'm seeing in the discussions:
I have an unlocked iPhone 4S (bought in France) and use it with Vodafone in Portugal. I was using the same SIM card that worked perfectly fine for over a year on my previous iPhone 4, and it also worked just fine in the 4S... until I updated to iOS 5.0.1.
The very next day I started having connections issues and invalid SIM card errors - requiring a reboot to temporarily fix it for a few minutes, until it lost connection again - the iPhone would still show it had a few bars strength, but was actually unable to make calls or use data. After a while it would go back to invalid sim message.
I replaced my old SIM card, and I though that was it... It was working fine.. until after 3 or 4 days, I find once again that I had a Invalid SIM message.
I've read reports suggesting that this might actually have to do with using other chargers than the official Apple 4S one - it sound kind of crazy, but just in case, I was also using a 3rd party charger when those issues arised for the first time. Anyway, I was now using my previous official iPhone 4 charger when I got the new error with the new SIM card.
Also, although the iPhone recommends using a non-locked SIM Card, mine has always had a PIN, and always worked through activations without a problem.
Other than being a real hardware problem with my new iPhone 4S (crossing my fingers it isn't!) my guess is that this is a software related incident - as this has just popped up after upgrading to iOS 5.0.1, and it would have been an amazing coincidence for SIM cards to go bust, or for the iPhone 4S to suddenly malfunction, afterwards.
Hope you guys can fix it soon, as well as the phone numbers not showing up the callers name in the contacts (that was a problem I was having from the very beginning, with iOS 5.0.0).