Facebook notifications do not open a browser window when clicked
I'm also having troubles with the native Facebook alerts.
They just don't work as advertised, that's why I was searching in the web and found this article http://lifehacker.com/5943851/glow-for-fb-stuffs-unobtrusive-facebook-notifications-in-your-menu-bar

That app did it for me :) you click the Notification Center popups and you'll be redirected to the corresponding subject, e.g. the photo, a comment or a message thread.