Morten,
You have multiple Facebook Connect extensions enabled on your site. If you open the HTML of the page you sent, and search for "all.js", you'll see it come up a few times. The first time is ours, the 2nd time is something else (I believe JomSocial). Additionally, a few lines above the all.js line in both cases is a line for appId, which is your Facebook application ID. In both cases, there is a different ID being used.
This is the cause of your problem. Please disable JomSocial's Facebook Connect by removing the API/Secret keys from their configuration area and disabling the JomSocial Connect plugin. If you have any other Facebook Connect extensions enabled, you may need to disable those too.
Hope this helps, and, after those are disabled, please let us know if you continue to have issues!