It looks like the screen is recognizing about a dozen touch inputs even if there is no physical contact.
The problem can be fixed by pressing the upper right hand button and making it sleep but I need a permanent solution.
This is definitely a hardware issue, not a Windows RT bug. The Surface RT user who has this problem on Microsoft Answers site refreshed the and re-installed all the patches/drivers/updates. Still has the issue. He also did a hard reset of the device and the problem appeared as soon as he was about to update all the devices.