Greetings!
This is not a problem with your phone. This is just another thing Android lacks comapred to other OS's. Call blackberry whatever you'd like but at least it has a simple feature of notifications for facebook.
What you need to do is download the app called "Bloo". Just keep that running and link it up in your message widget. It will give you notifications on comments/wall postings/when someone likes your status. The other regular facebook app will notify you if you get a message/invite. Well at least mine does.
Never check the notification through bloo just look at what the notification says and then check it through the normal app. That is the only thing we can do at this point.
I believe someone posted on here that if you make your facebook email your gmail address it would work??? but i dont know if this is true. Hope this helps you.