I just installed Mountain Lion, and I notice that the icons for Launchpad, App Store, To-Dos and Notes cannot be removed from my Dock — if I try to drag them off my Dock, they float back in.
Is there a way to hide or remove these icons?
I have not tried it myself, but I read in a review that they intentionally made it harder to accidentally remove icons from the Dock.
Trying dragging the icon a good distance away from the dock and holding it there for a couple seconds, it should show you some kind of "about to poof this" indicator, and then drop it.
At least, that's what I got from the review I read.