I just tried to pair my BT headset with iPhone but something odd happened. I tried to turn the Bluetooth ON (Settings/General/Bluetooth) but I couldn't... nothing happened - only gray scrolling circle (in place of the ON button). I restarted the phone couple of times... NOTHING!.

I was getting a bit worried and that point.

Then I tried turning the Flight Mode ON and activated the Bluetooth! VOILA!!!

The funny thing was BT worked OK now , but I wasn't getting any GSM signal, therefore I restarted the phone. Now everything works as it should! Excellent!

Edit:
Later I noticed that the signal always disappears when you return from Flight Mode and reappears when you make the call, so I guess it's just a bug.