Jussi,
That's very strange that it's just the FB buttons and not the Google + or others. The tag {JFBCLike ..} that's being inserted looks right, so something is just preventing our code from replacing that tag with the proper code.
Can you verify that the JFBCSystem plugin is enabled? You may want to re-order it to be in a higher ordering (first) or lower ordering (last) to see if that has any effect on things.
Strangely, if I view your page using a different template, the Like button works:
www.sanfordvet.com.au/?template=rhuk_milkway
Not sure if there's anything in your template settings that could be a problem, but it may be worth looking/changing some settings just to test.
Let us know if that doesn't help, and if possible, we can try to login to the admin area (if you're ok with it) and try to debug further. If so, please Private Message us some admin credentials. You can PM me by clicking the arrow under my picture (<----) and hitting the mail icon.
Thanks,
Alex