Hmm. Never a good way to start a support answer, but unfortunately, I'm not sure of the exact cause.
I just tried to login on your site using the exact version of IE that you mention, and it seemed to work like normal (no error). However, not all issues can be recreated by us. Can you let us know the following:
* Can you try IE on another computer?
* Can you try a different Facebook account?
* Can you delete your cookies and cache from IE and try again.
* Can you delete the Joomla cache (Tools->Clean Cache) and try again.
Sorry for all the 'try this and that', but it's the best I can go on right now. I'm also assuming this works fine for you in Firefox and Chrome (or other browsers). My hope is that the clearing of cache above fixes the issue. I researched the Knowledge Base error you reference, and the issue shouldn't be happening based on how the Facebook Javascript modifies the page.
Another thing to try is simply disabling the Login module and seeing if the error persists (it sounds like it's all the time, not just when you try to login). If it still happens, try disabling the JFBCSystem plugin. If you still get the error, then it's not related to JFBConnect, and I'd recommend disabling other Javascript plugins/modules until the issue goes away.
Hope this helps, and please let us know what you find!
Can't connect with IE 8.0.7600.16385
