Part of Facebook's July Breaking Changes was that all Like button's must have a full URL (including the
yourdomain.com/ part). If you are adding the Like button in a way that doesn't include the full URL, you'll need to fix that.
For more information on the changes, see our
Facebook's July Breaking Changes
blog post.
If none of that helps you figure out the issue, please let us know how the Like button is being added there: Our JFBContent plugin, the JFBCLike module or the {JFBCLike} tag and we can help further.
Thanks,
Alex