Facebook push not working I have an iPhone 4 with iOS5 and Facebook and Messenger push notifications are not working for me, or they're delivered hours after they should be.

I had jailbrake on iOS 4.x and always assumed that was the case for me not getting push notifications, but the problem is here again on a freshly restored phone with iOS5. All my settings are correct (i.e. notifications are on etc.), I tried the same thing on an iPad 2 with iOS5 and notifications work instantly.
You are experiencing something most of us do – the Facebook push notification server is notoriously unreliable. See this Daily Buggle article for both confirmation and a possible workaround using Boxcar.