We do monitor the FB API forums, but if there's a specific thread that you think pertains to how we're using the API and what may be causing your problem, by all means share it.
Our
Joomla Facebook Connect
demo site continues to work fine with IE for us for multiple versions from multiple computers. Please test yourself and let us know if it doesn't for you. Additionally, I would continue to recommend trying a much less 'flashy' theme over the JA or RT ones and try the default Rhuk template (I incorrectly said Khepri below which is the admin template). That way, you can discount your theme and we can investigate different possible causes.
The JFBConnect app is intentionally including an older version of the API as there have been versions that have caused severe issues. This version we've tested thoroughly with our application and feature requirements and have found it to be a good match. While we do plan to upgrade the included API in an upcoming revision, we don't want to do it willy-nilly. The API I'm speaking of here is the PHP library included. That is separate from the Javascript API which Facebook updates regularly (and does cause stability issues with in the process).