I know this is an older post, but I thought it might be worthwhile adding what I know, given I stumbled on this by Googling the issue. Maybe this will help someone.
So, my phone also had a faint, almost airbrush-like, blue spot towards the center of the screen. I noticed it about 4 hours after buying the phone yesterday. My problem was that it was a sometimes issue and it didn't always show up. I had my friend take a picture of it, to help prove it to the Verizon store where I purchased the phone, and I went back and they went ahead and just replaced it. The key is to make sure your screen does it in store. That may mean sitting in the middle of the mall/store/your car and continually turning your screen on and off until it does it, like I did.
It is also worth noting that the spot became more pronounced the longer I had the screen on, so after about 10 min of it being on (if even that) it was pretty obvious and the sales rep wasn't even squinting to see it.
Also, I don't have a case, yet, and my phone did respond to the spot between the HTC and Beats logo being pushed. I haven't had the guts to try it on the new phone.