My first EVO 4G LTE had a screen flicker issue and it was driving me crazy. I had the same issues described in this post. It only does it on solid grays, like in the empty boxes in the market, in the background of dialog boxes and in the task switcher.
I exchanged it, and my second unit still had a screen flicker. It wasn't as bad (my first phone gave me a headache if I stared at it long enough) but was still present.
Yesterday I was using my phone non-stop for most of the day (love the battery life btw) and looked at the battery stats and the screen was on for about 4 hours. I noticed at the end of the night that the screen flicker was pretty much non existent. I looked closely this morning and and it still wasn't flickering.
Maybe the screen has to be "broken in?" Possibly it is just the nature of Super LCD screen technology?
I put in a support request to HTC to get it repaired, but I think I'm not going to send it in. It looks fine to me right now.
EDIT: Nevermind, flickering is back. Sending my phone to HTC. Grrr.