Graeme,
It's likely a CSS issue with an older release of JFBConnect that you're using. LinkedIn has changed their buttons over the last year a few times, and there are numerous issues you may run into if you're using older versions of JFBConnect. The latest release is v6.0.6. If you're on that version, or any of the v6 releases, let us know a page we can look at and we'll gladly help investigate further.
Thanks,
Alex