I'm replying really late but I just noticed this post. It's peculiar to Facebook (and probably some other apps but the Facebook app is immensely popular and free so it's most noticed as failing to display notifications). It really must be, as previously mentioned, in the way Facebook implements push notifications. It's worth noting that with the iPhone alone, sometimes FB notifications and badges just quit working though correctly configured. Phone restarts, FB app reinstalls, turning off and then back on notifications for FB, nothing works. Then one day it just starts working again after apparently nothing has changed. This issue has improved over a couple years with regular FB updates. However, I have a Pebble, too, and FB notifications on Pebble are intermittent as well and remain so. And on my Apple Watch, I've never had an FB notification work.
Seems Apple apps and apps with Watch app functionality are the most dependable notifiers on Apple Watch, although most third-party push notifications work fine for me, Watch app or no Watch app. Presumably FB Messenger will work well enough too, as it has a Watch app feature now.
If you're generally only getting text message and phone call notifications on your Apple Watch, not emails, or Find My Friends, or calender or reminders alarms -- Apple apps that should notify the watch no problem -- you can go into sounds and haptics settings and turn off cover to mute. This fixed it for me when I was only getting text message, phone call and activity app notifications. And it still works as a fix in watchOS2. The forum poster who provided the advice says once you're getting your Apple Watch notifications like you should you can turn cover to mute back on and all fixed notifications will still work. I haven't tried that because I never use cover to mute. I just left it off. But if you use that feature, turn it back on after your notifications start working. If they quit working again you can always just turn it off again.
Still, Facebook, notifications are quirky and I still don't get them. Though, like I mentioned, I've had problems with FB notifications on a Pebble, and on the iPhone itself. And I think it's pretty telling it's a Pebble notifications problem too. So I wouldn't sweat Facebook. If they add a Watch app feature, maybe that'll get it consistently working.