Bought a Nexus7-2013 last Thursday.
Going to return it today since I noticed intermittent problems with touch: after shaking the tablet, there are multiple rows where touching causes extra touches to register elsewhere up or down the screen.
At first I thought it was my fingers hitting the wrong rows on the on-screen keyboard but after running Multitouch Visible Test, I was able to confirm that multiple touches were actually registering 1/2-3/4" away from where my finger was and it affected the problematic rows across the whole screen.
After being lucky on my original N7 with the "worst" problem on it being the relatively minor LCD becoming a little loose around the middle (I decided to stick to my first N7 instead of risking getting a replacement with one of the much worse problems), looks like it is my turn to get a lemon for my first N7v2. I hope the touch problem is not as much of a serial issue as the loose mid-screen was on the original.