For at least the last two iOS generations, I have had the problem where the application badges won't update unless I open the applications themselves (for example, when I read a Mail message on my iPad and the iPhone mail application badge won't update showing the message being read). Very annoying. I've put up with it for a long time. I've tried everything to remedy the problem but to no avail.
I decided to rely solely on the Notification Center itself and to display the message on the lock screen. This is sufficient for me.