I'm having the same problem, If I hold the end key to select options the "airplane mode" is off. If I got to phone settings the "airplane mode" is off and I still cant make calls or receive them, or any txt msg as well. When I got to make a call it says please turn off airplane mode. And the only two places I know of that gives the option of turning it on/off they both say that it is off.
I have been having to power cylce to get it to work again, about 40sec after fully powering up I start to get like 30 voice mails and txt msg all at once that I missed during this "airplane mode" that was active I guess(even though the phone said it was off)
I just did a hard reset yesterday and so far so good. If it continues I'll go have them give me a new phone. If not Im trading this in for the hero.
I had a feeling something like this would happen, I hate buying the first generation of any electronic device. All these damn bugs that need to be fixed.
My only other complaint is that some apps randomly crash and are forced to stop.