Mountain Lion Notification Center glitches
I'm having the same issue as Arnold. The problem might even be slighty worse for me; opun freezing, I can only use keyboard input; mouse clicks aren't registered anymore. I use QuickSilver to launch a terminal and running "killall -9 Dock" two times kills the dock and releases the mouse. After a couple of minutes the dock is relaunched. Also sending the HUP or INT to Dock will kill it. Sending the TERM signal doesn't though.

I found that the problem can be circumvented by rebooting the system and after reboot ensuring that the first thing you do is to open the notification center. I think that by sleeping your mac without having the notification center open before that is what makes it crash.

Sadly, I didn't find any way to check what's keeping the Dock process busy. It doesn't seem to be the notification centre itself that's crashing (it keeps responding to mouse clicks while nothing else does) but the Dock. So far the only thing I came up with is that this is a problem with launchd, but that doesn't help a lot because killing launchd will kill every application you have running.