Unfortunately, this is an issue with Joomla itself. There's no way for JFBConnect to 'know' which one is the canonical (correct) URL. The extension will assume that if the URL is being accessed, it's a proper URL.
There is some logic in JFBConnect to try to guess the best URL for the page, but if there's no menu Itemid associated with the URL or anything else for us to use, we simply use the current URL. In that case, there can be a split between the share count and comments between the different URLs.
Unfortunately, there's no way within JFBConnect that we can fix this. It's also why there's a proliferation of different SEF extensions which fix many of the duplicate content issues of Joomla. There's a project underway as well to replace the core Joomla router with an improved one that shouldn't generated duplicate URLs for the same page. We're excited to see that project move forward with what looks like a release later this summer.
I hope that helps explain,
Alex