Gregory,
I just tried to register on your site and saw the error you mention. We haven't seen that problem before. I have a few guesses where to look, but don't have a specific solution.
The error your seeing only happens when, for some reason, we can't 'connect' the users Facebook ID to the user's Joomla account we created. The only time that should happen (which we've honestly never seen) is if the Joomla user account can't be created. Can you check if you have any Authentication, User, or System plugins that somehow restrict new account creations by any criteria? If not, can you check if any of those plugin groups have a plugin which is meant to redirect the user after registering, or at some other point of registration or logging in?
In general, it seems like something on your site is interfering with our creation of the Joomla user. Once you find that, it should help fix the problem.
Finally, another thing to try is, in the Configuration -> Facebook API area of JFBConnect, enable error reporting on the front-end. If you're seeing any new errors reported from Facebook when you try to login, let us know, and that will help come up with other possible fixes.
Thanks,
Alex