I found this solution on XDA Developers
Fixed my touch screen problems!
I purchased my Nexus 7 from Staples during business trip to San Francisco. My device started having touch screen issues after few hours. Factory reset did fix it and I liked the device a lot so I didn't return it as I thought touch screen issue was just a SW glitch. Issue came back at the airport . Unfortunately I didn't have time to return the device at that point. Issue wasn't manifesting itself all the time, but seemed to come up every time I plugged the device in charger. Symptoms were exactly as in this video:
Nexus 7 Touch screen problem defect - YouTube
and the other one in which multitouch is demonstrated. I suspected different applications as a reason to the problem as well as faulty charger. Then I found this thread and became assured that this must be a HW problem.
As I'm living in Finland and don't know when my next business trip to USA will take place I decided to try and fix the problem myself. I took off the back cover and touch screen worked perfectly. Initially I suspected grounding problem but pretty soon came to conclusion that it can not be the case. The problem in my case was the "sponge" pushing (what I assume is) display / touch flex. I have marked that in the attached picture. Even a very light touch to sponge caused touch screen to go crazy. As I don't have the luxury of immediate warranty repair I decided to remove the sponge and my Nexus 7 has been working flawlessly ever since. I can even charge and everything works as expected. When I started charging the device I placed my Nexus 7 on the table. It probably caused slightly increased pressure on back cover and therefore to "sponge". After removing the sponge I can't see any of the touch screen problems I was having. Couldn't be happier as I don't have any of the other problems people have found and device is working as it should, at least for now.
I don't encourage anyone to do what I did, but if you are in the same situation as I was with imported device, you can try to take off back cover and see if the problems are fixed. You should be very careful though not to break the device especially when it's powered on with back cover off. Hope this helps someone.
EDIT: 22.8.2012. Forgot to mention, that turn of WiFi if using device with back cover off. Turning off NFC and GPS won't hurt, although GPS is receiving only. Reason is that antennas are located on back cover.