The problem is that you have multiple Facebook Connect components, modules, or plugins all trying to work on that page. If you open the HTML, and search for "all.js", you'll find it's included 5 times. Ours is at the very top, and we're including the da_DK language version of it. The rest are lower down, and all including the en_US version.
Additionally, if you search for appID, there are 2 different Facebook Application ID's that are being used.
These 2 issues (mainly the 2nd) combine to completely confuse Facebook as to what to do when a user tries to connect (which javascript code should it execute, what app is the user trying to connect too), etc.
You should:
1) Disable JomSocial's Facebook Connect integration - Remove the API/Secret Keys from their configuration area
2) Find the other sources of inclusion of the above and try to remove them.
If you run into any features you were relying on in the other extensions that JFBConnect doesn't provide, or if you run into any further issues, let us know!