It happens to me too on my grouper Nexus 7 2012, mainly in the center-right of the screen. I activated the option to see the input and I can clearly see it.
I know the most obvious cause of this is hardware issue but the strange thing is that mine does it only after a certain time without a reboot. As soon as I reboot it stops for a while. So I guess it's not 100% hardware or caused by overheating. And if I just put it aside instead of rebboting it the minute I wake it from sleep the problem is still there, only a reboot can help. And it doesn't do it on the recovery.
The other thing I should mention is that I have issue with the headphones on the tablet and I have to "twist" lightly near the connector to make the sound play on both channels. This is a known hardware issue. I had the touchscreen problem before that so the "twisting" is not the cause of it (and again since a reboot makes the problem go away I guess that's not it)
I tried many roms with the same problem and it happens only since I have f2fs (must be a coincidence) and I am now on 4.4.4 saberdroid and I have the same issue.
Is there a possibility that it could be anything else beside hardware???.... I will try 100% stock soon but I wanted to find if anyone had ideas about this...
Thanks! (if it doesn't work I might have to buy a Shield tablet, poor me!)