Q: iPhone backround services?

I've noticed that I don't appear to be getting notifications in the way that I used to when using my new iPhone 5s.

For example, when someone sends me a message on Facebook, I used to get the little red and white symbol over the app's icon to let me know. This now doesn't happen until I go into the actual app and come out again. Then it appears.

Similarly, I've noticed that the Podcast app doesn't auto-update (despite having it configuered to do so) and a few other apps also don't show any alerts UNLESS I go into the actual apps and come out again.

It's almost as though I have some sort of 'backround service' setting diasbaled.

Can anyone help?

THANKS