I have installed and enabled the facebook plugin, and entered the Facebook API app ID and secret into the plugin. I have also entered the facebook app ID into the Social API section within the template, and enabled it.
When you go to Login in the front end it shows and seems responsive, but if you click it nothing happens.
You should not mix our solutions with 3rd party fb plugins. Please disable fb plugin you are using and write back - I'll check what is the problem source.
From what I see, everything looks all right on our side... It looks like a strange problem with facebook istelf. I'll ask our devteam to take a look into it.
One of our developers suggested to check if APP ID is entered into template settings. Also please disable SEF URL's - will the problem disappear when you will disable it?