The problem is that there is another extension on your page that's re-including the Facebook Javascript library. Unfortunately, I can't tell what extension it is. The line in your HTML that's causing the problem is:
<script src="http://connect.facebook.net/el_GR/all.js#xfbml=1" type="text/javascript"></script>
Directly under that is some Javascript for Hikashop. You also have a Like-Box module at the bottom of your site that may be including it as well. It could be from some other extension or directly in your template as well.
You'll need to diagnose what extension is including the Facebook Javascript library again and disable the extension or it's inclusion of that line. JFBConnect needs Facebook's library initialized in a very specific way, and the line above is conflicting with that.
I hope that helps get you started, but if not, let us know,
Alex