Something weird is going on in your site. Looking at the HTML on your home page, there's a chunk of code that's being duplicated, our JFBConnect code included.
If you look right before the closing of the head section, you'll see duplicated code, starting with a Javascript file inclusion for "ajax_1.3.js", which comes from JomSocial. Then, there's a chunk of our JFBConnect code. Then it repeats.
In our chunk of code there, we setup some information for where the page should redirect. If it's on their twice, and especially if the links somehow are different (they weren't when I looked, but I can imagine they may be), random things may happen.
Even more odd is that this only happens on the home page. When I went to a handful of other pages inside your site, the code wasn't duplicated.
While I don't have an answer for you, it seems like something is behaving strangely in your site, either through redirects or repeated loading of some plugins (not just ours) that shouldn't be. I can't tell you where to start diagnosing this, but hopefully, this gets you started. I'd definitely recommend only enabling the Global Configuration cache, for now, and disabling the System - Cache plugin, as that is definitely tricky sometimes.
Good luck, and keep us posted,
Alex