Pretty much the same issue just popped up with my G2. It's been perfect for me since I got it around october 7th. But starting today, I have an area on the screen similar to what marionico posted a picture of. Mine is offset more towards the upper half of the screen though. Pretty much inline with the power button. In addition to that, knock knock does not work at all anymore. The dead spot is present throughout the UI and all apps i've tried so far. And turning the screen off then on again does nothing for this issue. Seems to be a common problem from a quick google search and I hope it's just software related. (even though it's not looking that way so far)
Before the G2 released, I told myself that I would never get another LG smartphone because I've always had bad luck with them. (LG thrill, optimus G, Nexus 4) But the G2 looked very promising and came with some of the best specs over all. If this ends up being a device cripling issue that LG won't/can't do anything about, I'm done with LG for good.