This appears fixed now. The issue was with Artio SEF. It was SEF'ing a callback url from Facebook into something that wasn't working. After telling Artio to skip JFBConnect for SEF URL generation, it seems to work properly.
Please test, and let us know if everything's working as expected. We'll create an FAQ about this issue, and investigate allowing SEF URLs within JFBConnect (there's really only one URL created that user's see). If you want a better SEF URL for the registration page, feel free to update Artio to use Joomla's SEF handler on JFBConnect.
Finally, if you're happy with the extension and/or your service and support here, we'd love a review on the JED:
extensions.joomla.org/extensions/communi...are/communities/7215
Thanks,
Alex