Looks like this is a "feature" and not a bug with iOS6. I found the paragraph below from this article http://support.apple.com/kb/HT1664 on the support site. I tried it out and it works fine as long as I answer using my Bluetooth device vs. answering on the phone itself.
"When your iOS device is connected to a Bluetooth accessory, all outgoing calls are routed through the Bluetooth accessory by default. Incoming calls are routed through the Bluetooth accessory if you answer the call with it, or through your iOS device if you answer with it. In some cases, your contacts list transfers to the car kit and you can start a call by looking up a contact on the car kit's display."
You are correct, it works when I answer using the Nokia Bluetooth device, though its button is extremely inconvenient. If I press it a tiny bit longer than neccessary it drops the call
In iOS 5.1.1 I used to answer using the iPhone touch screen and get the sound in the Bluetooth device, it worked perfectly but unfortunatelly Apple decides what's better for us without asking us and not leaving any alternative.
Any way - thanks a lot for your answer! I really appreciate it.
You solved my problem.