The authentication worked for me. However, during the authentication, it looks like there is extension (likely for SEF) that is altering our authentication URLs. You'll need to disable that extension from altering our URLs. When it does so, they look like:
component/com_jfbconnect/1a8fde096da2676d226c3f3855611b67,1/provider,facebook/return,L2Vu/task,authenticate.login/view,login/
That's invalid and can cause some problems with the codes that Facebook returns to us.
I hope that helps get things fixed up,
Alex