I always use the Nexus 7 held in my hand so that's not a solution for me. However, a quick test shows that the problem is worse with Nexus on the table and improved if the finger of my holding hand rests around to touch the edge of the glass screen itself.
My options seems to be:
leave one finger touching non-active area of screen to earth it - some success but limited
downgrade Android to v 4.2 - I guess this is what I'll do
seek a replacement - I don't know how I would even do this? Go to the vendor, who sells everything from ink to vacuum cleaners, and demonstrate an intermittent problem using some small-time testing app? I'd be relying on their goodwill...
Looking forward to hearing any of your solutions, y'all!
I had the exact same problem with the unresponsiveness unless I touch the glass off the screen with another finger or the thumb of my other hand.
It turned out to be the screen protector! Spigen Steinheil Ultra Chrystal screen protector was the one I removed.