Brian,
Earlier when I tested, I hit the Recommend button in the sidebar and the comment box properly appeared. I'm not sure if uninstalling/reinstalling would have had an effect on that. It may have simply be a caching or update issue on Facebook's end.
Generally speaking, JFBConnect doesn't care about subdomain vs root domain. JFBConnect will simply choose the URL of the current page and assign Like's to that page.
So, with all that said, the Like count for
radio.ourplace-sites.com/ and
www.ourplace-sites.com/joomla16/ will be different. It will depend on when/where the user clicked the Like button. If they did it on the sub-domain page, that is where the count will be applied to. If you want, you can 'force' the URL to always be for the subdomain by using the JFBCLike parameters. Then, even on the /joomla16 page, the count will show for the subdomain. I believe your subdomain truly has 198 Like's.. that's a good thing.
Finally, you can try the
Facebook Like configuration tool
and test yourself. Put both URLs in the box and you'll see the different counts. It's not a JFBConnect thing, it's a Facebook thing.
Hope that helps explain, but if not, let us know,
Alex