I have the same issue on one of my websites. Didn't find a solution to the problem yet, but in my case 2 things happened before this bug appeared (the FB sharer button worked fine before):
Introduced og: tags in the head section of my page (FB debugger shows all of them are OK, the page looks fine in the debugger tool)
Introduced the share button for twitter, this works fine
update: found the problem finally: it looks like you can only share things on FB if you have a Facebook AppID, so you need to create one on https://developers.facebook.com/ After you create the Application, get the embed code again and the AppId will be automatically included into the code snippet they generate for you. Your code will look something like this:
<div id="fb-root"></div>
<script>(function(d, s, id) {
var js, fjs = d.getElementsByTagName(s)[0];
if (d.getElementById(id)) return;
js = d.createElement(s); js.id = id;
js.src = "//connect.facebook.net/en_US/sdk.js#xfbml=1&appId=3#########4&version=v2.0";
fjs.parentNode.insertBefore(js, fjs);
}(document, 'script', 'facebook-jssdk'));</script>