Hi,
We didn't built those buttons, we have used AddThis.com service to get the tiny buttons on the left, and we used the developers.facebook.com to generate the "LIKE" button.
So they should all work properly, the bugs or errors are unexpected.
Are you working in a live server?
Because if you are in your localhost, the image can't be grabbed by facebook. You must be in the live server.
And also make sure your joomla is open to public, there shouldn't be any password protected environment, and the URL of image should be browsed by public.
Cheers.