I changed my code to the following:
<iframe src="
http://www.facebook.com/plugins/like.php?href=[[~[[*id]]? &scheme=`full`]]
&layout=standard&show_faces=true&width=240&action=like&font&colorscheme=light&height=80" scrolling="no" frameborder="0" style="border:none; overflow:hidden; width:240px; height:80px;" allowTransparency="true"></iframe>
Now this works on my home page but not on my product pages.
How can that be?