Thank you for the answers. I don't think seeing your computer will help too much, unfortunately. Everything looks fine, code-wise from our end and I'd assume it'd look the same through your browser.
One thing to try, though it shouldn't help, is to try removing the inclusion of the jfbcchannel.php file you mention above. That file is explicitly for IE browsers and is recommended by Facebook to include it. However, removing it should still work, but may decrease page load times by a few milliseconds (nothing drastic). To remove the file, edit the /plugins/system/jfbcsystem.php file. Around line 161, you'll see:
FB.init({appId: '{$appId}', status: true, cookie: true, xfbml: true, oauth: true, channelUrl: '{$channelurl}'});{$subs}{$resizeCode}Update that to the below line, removing the channelUrl parameter:
FB.init({appId: '{$appId}', status: true, cookie: true, xfbml: true, oauth: true);{$subs}{$resizeCode}After updating, clear your Joomla cache and try again.
Let us know how that goes. We're still testing. We have one main IP here, but multiple Windows computers (Win7 and XP) and will see if we can cause the problem to appear.
Thanks,
Alex