I'm also in the boat with those that are getting Error:the plugin is not connected to Facebook.
When you go to connect get Given URL is not allow by the Application Configuration: One or more of the given URLs is not allow by the App's settings. It must match the Website URL or Canvas URL, or he domain must be be a subdomain of one of the App's domains.
All information is in the Apps > <App Name> > Basic as well as I've toggled on and off each of the items that were suggested in the forums. Picked up the latest copy of the PLUG listed in the forums and this has not fixed this issue as well. I'm running WP 3.6.