Brand New iPad 3 has a jiggly screen and black boxes across the screen in different apps

My mother purchased a brand new iPad 3 about 1 week ago.  The screen has begun to shake while she is in the apps.  (This is not the shaking that icons do on when you hold an app down so you can rearrange.)  When this happens the screen will go blank when her hand is near it and reappear when she moves it away.  Also, in some apps, I have experienced this in the App Store and Facebook, black boxes cover the screen so that you cannot see what is behind them.
We have tried shutting it down completely, but that doesn't seem to be a fix.
I have been searching for others with this problem and haven't found any.  Help would be appreciated.  Given the sporadic nature (but often enough to be a bother), I'm hesitant to go to the Genius Bar for fear it wouldn't do it then. 

I've had the same problem with Big Black squares covering the screen. And a few times the screen has split vertical in the middle and pushed everything in the on half a little down, making it very difficult to read text as the lines was cut in half.
I first experienced it in Mail, and then in Safari. I noticed that it is only covering content, not the App bar and When I scrolled down, the boxes were staying On the spot On the page. I figure it must be a software problem as it moves alting with the rest of the content, so I tried uenig Chrome instead, but yesterday the same ting happened.
I have tryed to take a screen dump, but it gets completely black
Its not warm When the problem occours.
Anyone with a solution?

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