I've scanned this thread. My impression is that there's more than one theme in the thread. Some people have a relatively simple defect -- a screen that's clearly loose. That may be related to dropping the phone or "bad luck" and it sounds straightforward. In some cases there may be loose screws at the base of the phone (these are very tiny screws, few people have the right tools to tighten them -- I'd let the Apple store do it).
More people, especially more recently, have a distinct "pop" sound with light pressure over a part of the display. It can be any part of the display. This sounds like either a design or manufacturing flaw or both. We'd need an expert in iPhone assembly to contribute. I can imagine a small structural deformity related to dropping the phone or imperceptible "pocket-bend" or a problem with screen bonding chemistry.
If you squeeze firmly (but not TOO hard) over the pop area the problem will often clear for a few days to a week (which sounds like a bonding issue). I suspect Apple techs are "fixing" some phones this way.
When an iPhone is replaced under warranty Apple typically distributes a refurbished phone, and it sounds like they often have the same issue. It may be that Apple still doesn't understand the problem and that they haven't tested refurbs for the defect. As of Nov 2015 I don't think Apple has distributed a fix to service centers.
The fix may be expensive. It may require replacement of the screen/touch sensor, or frame replacement or even both. From my experience with similar defects on iMacs once Apple understands the problem they will fix it under warranty but if the repair is costly they may or may not do a post-warranty repair program. (Long discussion threads seem to help, contrary to what's often said here I think Apple does monitor long threads).
I'm going to take my phone to a local Apple store for review. If they don't know the cause (or are not authorized to discuss it) I'll hold onto my phone -- but I'll keep a record of the visit so I have proof the problem occurred under warranty.