The Nexus 7 has a quite faulty touchscreen which is prone to ghosting and similiar.
If you got your device rooted, you could go for Parrotmod, which seems to fix said problem:
https://forum.xda-developers.com/nexus-7-2013/orig-development/beta-1-parrotmod-improve-2013-nexus-7-t3375928
Another soultion would be to flash a new touchscreen firmware, as shown here. However, I have not tested this yet.