Thanks for your patience. We've found the issue, but I still don't know the cause. The problem is that on all pages that are failing, there are 2 <head> sections. The first section is correct. The second section is being inserted by something that just puts the following on the page:
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
</head>
It's invalid HTML to have 2 <head> sections on the page and JFBConnect intentionally stops doing some things.
You'll need to find what's inserting that extra head element section on the page and fix it. Then, all the social buttons should start working.
I hope that helps,
Alex