There is a well-documented defect in the G2 software that surfaces as erratic touchscreen behavior. I am active on XDA and Android Central forums trying to identify the cause of this issue and trying to get LG and VZW to address it with a software update. I have also posted on social media attempting to get the attention this deserves. In addition, I have created a "Voice of the Customer" defect report with LG.
I have provided links below for your reference rather than duplicate all of that text in this post. Just these two threads alone currently have over 15,000 visits by G2 owners, many of which have already observed this defect.
Here is the XDA thread that I started that clearly describes the problem, complete with YouTube links and the latest on this G2 defect:
http://forum.xda-developers.com/showthread.php?t=2521663
Here is the Android Central thread to which I contribute:
http://forums.androidcentral.com/lg-g2/317709-g2-touch-screen-issues.html
The G2 community is calling for LG and VZW to weigh-in on this issues. A large number of G2's are being returned, which can't bode well for VZW or LG.