David,
Facebook has a few ways to associate a Like with a page. The Like button itself can specify a URL for the like-click to be associated with. Also, the Open Graph tags can specify a destination URL. Sometimes the URL is simply for the current page, but sometimes it's for the destination page (think of 5 articles in a blog layout, each Like button should be for the final article, not the current page.
JFBConnect enables it's Open Graph support by default, which tries to determine the best final URL, title, description, and sometimes even image to use for any Like's that are clicked. If you have another extension managing Open Graph tags, you may want to disable our integration. You can do so in the Social Configuration -> Open Graph area.
There should only be one extension inserting Open Graph tags though, because if each one inserts conflicting data, Facebook can get confused (as you've seen) and have unexpected behavior.
Hope that helps, but if you need more info, just let us know,
Alex