Frank,
Not sure why you're having issues. I can recreate them by clicking the Login With Facebook button on your site though, so you're not crazy
Here's a couple of things that may be contributing to the problem that I can see. If it's possible to disable these (temporarily) that would be great
* Your template looks to have some Facebook features built in. When I open the HTML, in the body tag, I see:
data-config='{"twitter":1,"plusone":1,"facebook":1}'Not sure what that's doing, but it's likely causing the Facebook Javascript library to be re-loaded somewhere. If you can disable other Facebook integration, that'd be great.
* All the Javascript tags have been replaced with <script type="text/rocketscript"> Never seen that before (may be related to Cloudflare). If it's a Joomla extension, can you try disabling it. Some 'optimization' scripts can cause conflicts with Facebook.
* Cloudflare - They heavily cache things. While that shouldn't be the problem, eliminating them as the source would be good.
Again, these would be temporary measures to narrow things down. If you can test and let us know if any helps, we can help re-enable the feature. Beyond that, a bit dumbfounded, but we'll get it!
Thanks,
Alex