Clark,
Sorry to keep asking more questions, but what SEF utility are you using on the site? The login URL being generated is strange, and could be the cause of the problem. If you don't mind changing a line of code, I have a suggestion below. I don't think this will fix the issue, but might get us farther along, and help to narrow down the problem.
In the components/com_jfbconnect/helpers/facebookhelper.php file, line 27:
function getFacebookUserLoginLink()
{
return JRoute::_("index.php?option=com_jfbconnect&task=loginFacebookUser");
}
Change the return line to:
return "index.php?option=com_jfbconnect&task=loginFacebookUser";
Depending on the SEF component, this may not change a thing (just ignoring JRoute), but it's an attempt. Once I know what you're using, I'll try to install it and start trying to figure out the issue. If there's a way inside the SEF component to ignore any URLs from JFBConnect, that'd be swell to too