I have purchased 3 iPhone 5s's in the last six months all three had this issue. The first one was purchased for T Mobile's service and they replaced it with a new one from T Mobile, that solved the problem. I no longer have that phone. I then purchased one for my mother, it had the same issue, I returned it at the Genius Bar two times before getting one without the issue. Finally, my personal cellular phone purchased three weeks ago had the issue, I replaced it from Apple directly through the mail, it still had the issue, then at the Genius Bar (they let me look at 3 that day) all displayed the issue, I picked the least affected of the four, and then once more through the mail, no luck, it is still displaying the lines.
The interesting part was my latest interaction with the Genius Bar (May 12, 2014). The genius first stated that she did not see the lines and if I looked at four of them and they all displayed the problem that it was normal, not a defect, and it therefore must be to specification. It is the same as arguing that a faulty ignition installed on 10 cars is okay because they are all faulty. I did mention that I was being a little nit picky, but that I also expected a display at least as good as the iPad Air's, and the competitions', to which she replied that these were all different technologies. This statement was followed with a statement that all LCDs diplay this line problem (a direct contradiction to her previous statements). I attempted to explain that what I was seeing was not the grid of the display but distinct vertical lines that most likely is a hardware issue. She still did not believe it. So I followed it up with displaying the image contained in this forum. The answer at that time was that the flickering was an optical illusion. I answered then why is the image static on one of their display models (they had one that did not display this problem). To which she returned to the well this meets our specifications so we are not going to replace it. There were some comments about how much it costs Apple and that other customers need their phones replaced etc. In any event, she called her manager over who promptly mentioned that he would try one more time for me. I requested whether they would try to find one with a C serial number and there were none and they also said they had not seen any 5s's manufactured there coming into the store (south Florida area).
The one they brought out had the same problem. I tucked my tail in and went home with my phone. I called Applecare on the phone that night and currently have it elevated to the engineering department to see if they can do anything. My guess is no, they can't. But I will wait to hear the follow up in 30 minutes tonight. I just don't understand how this kind of quality issue can exist. It seems like this is something that has been around since the introduction of the retina display tech (or high resolution iphone 4 screen). I have therefore looked at 10+ phones and found 3 to 4 without the problem. I am sure this fits within their manufacturing tolerances, I just think it is garbage to call this acceptible, especially when other manufacturers do not have this issue.