Chris,
Yes, having another extension could easily cause what you were saying, especially if our "Automatically login Facebook Users" setting was enabled. JFBConnect could have been detecting that the user is logged into Facebook.com, but when we tried to log them into your site, it wouldn't have been able to communicate with Facebook properly due to the conflict. In that case, we'd try, fail, and then on the next page load, go through the same loop.
It could be lots of other things too, but getting rid of that conflict is step number 1 to narrowing things down.
I hope that helps, and you have things going now, but if not, let me know and we'll gladly help how we can.
Thanks,
Alex