Facebook has always been spotty with notifications with iOS 5 and 6. I do get them with 6 on occasion. But with 6 the notifications no longer make an alert sound which they did for me in 5 (I have a custom alert noise). I don't feel FB is integrated very well in iOS at all.
On a side note, I get Facebook and Twitter notifications but the default Tweet and Facebook sounds don't sound, I just hear the default iPhone alert sound even though I have selected the other sounds in the settings. Any ideas?