The lines mostly appear on grey colors. Lower brightness makes them easier to see.
Only time I ever see them while playing is when I look at the sky or something in Uncharted on a night/low light level. They pop up all over while watching videos (Dota 2 has an entire side of the map that is pretty grey). Also the Vita confirmation boxes that are grey/blue colored make them visible aswell.
There have been a few discussions I've found about it, and also about phones with similar screens that show the same issues. I don't think it's hugely common but I don't think it's as rare as something like this burn-in. My guess is a lot of people just don't notice it.
There were a few people with the issue
here. and from there someone linked a phone discussion
here. The vita discussion is a little disappointing to read because of the people trying to dismiss the problems as if the people that have them have hate the Vita or something.