I apologize for letting this post get lost. I originally did start investigating, but couldn't make heads or tails of what was going on. I put it off and it slipped my mind.
I just had some time to investigate more and found the problem. It's not an issue with JFBConnect at all but a known issue with your template. As noted above, JFBConnect creates a more full version of the URL for your article that includes a query parameter like:
id=84:test-share-facebook
There is a known bug in the Shape5_vertex template that chokes on that type of query string, even though it's valid.
For more information, see the bug report below:
issues.joomla.org/tracker/joomla-cms/6829
There's a suggested fix in the post, but you may also want to contact your template provider or check if there is an upgrade available that may fix the glitch.
I hope that helps,
Alex