Notifications for Facebook are janky at best on any platform, even Android. Usually with my Droid (Gingerbread, and never going to be upgraded past that, thank you Moto), if I had the little F in the notification bar, there was maybe a 60% chance that I had a for-real notification. This is mainly an issue with Facebook and their horrible lack of support for mobile of all flavors. That being said, I find notifications for FB to be completely unusable on WP8. When I have live tile on, it just keeps building the notification count forever until I have like 60 items no matter how many times I refresh the app or reboot the phone, and it always shows some random post in the tile that I put up from ages ago. At this point, I just turned off toasts, push, and everything else and just regularly open the app to check FB (having to manually refresh the feed every time). Annoying, but expected - the FB experience was horrible on iOS when it first came out (iPhone 3G), and damn near unusable on Android when that first came out. They fixed it enough over time, and will for this platform as well.
Notifications for Gmail and Outlook.com have been flawless on this phone, though - so that's really nice