I just wanted to post here to explain my situation if only for the sake of others in my situation being able to more easily find this thread with Google.
I have an iPhone 4 running 5.0.1 jailbroken using the latest redsn0w. I install my normal handful of jailbreak tweaks, and over time I discovered that when answering Facetime calls, the screen would freeze until the caller hung up. I couldn't escape the locked up screen at all, using the home button or power button. I could still "make" Facetime calls without trouble.
I never had any issues with iMessage.
Upon discovering the Facetime issue, my first thought was to remove Facetime-related tweaks on my phone. I had edited the plist to enable native 3G Facetime, so first I tried putting that back, but it didn't help. I installed My3G (which I bought before the 3Gvenice was discovered), same thing, no help. I tried removing any wifi-related tweaks I had installed (wicarrier, namely). No help. I removed an app I was using to download ringtones (not anyring), nothing.
Finally, I find this thread and realize it's COPIC. Deleted that app, rebooted, disabled facetime and imessage, rebooted, and enabled imessage and facetime and voila, facetime works fine. I even enabled 3Gvenice again and I have working Facetime on 3G.
Funny thing is, I only purchased and installed copic to begin with because cyntact (which I had purchased long before) had not been updated for iOS5. It has since been updated, and doesn't cause Facetime problems like Copic.
So yeah, if your Facetime freezes or hangs when answering calls on jailbroken iOS5 or 5.0.1, first thing should be to check if you have anyring or copic. If you do, remove them, disable facetime and imessage, reboot, and enable again.