I was thinking about this: the notification system of Stack Overflow is quite complete, in fact if my reputation changes or if someone answers questions, adds comments, etc., I can see it from the above status bar.
But many of this notifications will appear only when you reload the page, or change page, in general.
It could be a great improvement, I think, to make all these notifications appear through a push service. Something like what you see on Facebook or what you get on OS X using Grawl, I mean.
This way one could easily see when his/her reputation goes up or down, when new answers appear, when new comments appear, when a new badge is rewarded, and so on.
Does it make sense?