I don't know if this is phone or app related but push notifications rarely work. The only app that seems to be working is MSNBC,
[LIST][*]Facebook no notification of new messages etc[*]Twitter no notifications of mentions, PM's etc[*]Google+ Notifications only when you open the app[/LIST]
Anyone else have these issues? As I say the news ones like MSNBC,CNN seem to work fine the social networking ones don't

Simple I know, but, make sure notifications is switched on both in the phone settings and the app settings. Also make sure that the notification sound is switched on in the app