I opened the html on the page and searched for 'all.js'. That's the Facebook Javascript library, and if it loads multiple times, that can sometimes cause a problem. However, if you re-enable it, and search for all.js, you'll see that the appId in one of the Javascript lines was set to '' (blank). This will definitely cause problems because that's how Facebook identifies your page. So, JFBConnect was sending the correct App Id, the other thing was sending nothing, and Facebook was just getting thoroughly confused.
We deal with these types of issues a lot, so we know what to look for
Would love a review, but your subscriptions is a huge thanks already. Thank you!