I just received my new iPad 4 - 64gig - Verizon yesterday and immediately noticed a screen problem.
Mine seems to effect just the upper left one quarter of the display. When i scroll from right to left or up and down the upper left of the screen doesn't move with the other three quarters of the screen. It doesn't do it all the time but when it does it is very noticeable. It's like a fast blip and then corrects itself.
At first I thought it was me seeing thing but now, after seeing it many times, I know there is something wrong. My iPad 2 has never done this in the two years I've owned it.
I find it more prevalent in an app with text, like USA today and it is always just the upper left quarter of the screen, the rest of the screen scrolls just fine. I can't make it happen, it does it when it's least expected.
Not exactly what I expected and it will go back to apple for an exchange soon if it keeps up.