I like the notification system. An applet pops up whe I have a notification and I can choose to ignore it or go into the app for more information. What is wrong with that? I'm all for doing things better and maybe someone can show me a better way.
Up until recently I was happy with it as well.
Some sort of pull out tray like a few other mobile OS's would be good. The problem I have with iOS's handling is that it's a modal dialogue you must make a decision on. Either destructive (cancel - you may forget etc) or the positive action - which interrupts your current task. We need some way of being able to say cancel and look through it later when it suits us.
Many times we can be playing a game or browsing a website when a text message or an inane push notification takes precedence on screen. Or even better, an icon could gently pulsate in the status bar that relates to a certain app. Such as a text message, then we can be notified without being interrupted.