Damon,
We see the issue, and are going to have to investigate more. Basically, there looks to be a bug in Joomla 1.6 for how article links are created. From category views, the link to the final article includes the catid=xxx in the URL. However, the link created for the final article from other views does not have the catid. It's this 2nd type of link that we create for the Like button to actually 'like' when clicked. There's a lot of black magic behind the scenes of JFBConnect to try to make sure those numbers all link up, and it's something we'll have to investigate, and possibly submit to Joomla as a bug.
Ultimately, the final URL for an article, in our opinion and any search-engine minded admin, should be the same. This behavior obviously creates 2 different links to the same article, and that's not good.
Hope that helps explain, and thanks for pointing this out. We'll investigate further, but I don't think I'll have a good immediate answer for you, unfortunately.
Alex