The issue look like a failed or partial install of JFBConnect. The social network login buttons aren't showing up, which is causing the SCLogin module to get very confused. I've never seen anything like that. I can only recommend re-installing JFBConnect. Once you do, if you go to the JFBConnect -> Configuration -> Facebook (or any other social network) area, there should be an image in the "Login Button" area. On your site, it's just blank.
I hope that helps, but if the images still don't appear after re-installing, let me know and we'll look into things further.
Thanks,
Alex