Notification Center certainly has room for improvement and its myriad of vague settings can often lead to confusion.
To help you understand this feature of iOS a little more and get the most out of it, Rene Ritchie over at iMore has compiled an extensive collection of previously published tips and tricks into a single place, ranging from controlling app badges and sounds to customising the Today view.
There's plenty to read through and each guide includes screenshots to show you exactly what to do. If you're left frustrated with Notification Center, or notifications in general, this is a great reference to come back to.