I had a similar problem with a Samsung Droid Charge. I'd answer a call, and for a second or two, I'd hear audio from the call, but then that would quit, and, because I'd usually have the radio or music on, the radio would come back up. At first I thought it was dropping the call, but after a couple of times I realized that the call was still going, and that if I grabbed the phone and clicked on the bluetooth button on the screen, I could talk via the phone--kinda defeats the hands-free thing, but it worked.
Since the Galaxy is also a Samsung phone, maybe it's due to the same problem. There was a workaround that I used that stopped it, you might want to give it a try: With BT off, open settings->application->running services. Then start bluetooth, and go back to running servcies. Scroll through until you see the BT services (they have the BT icon). There were two, and one had "PB" in the title (possibly for phone book). Click on that guy and kill it.
And that's it. Worked...most of the time. Some times, I think whatever problem that thing caused remained if I didn't get to it quick enough.
I don't have that problem any more, as I'm running a leaked copy of Android 2.3.5. The Bluetooth works without issue, and the service names have changed.
Note that I didn't have any such problems with my old OG Droid, nor does my wife with her Droid 2 Global. Seems to be a Samsung problem with some car systems (google for it and you'll find other folks having issues, which is how I found this workaround).
Hope this helps.