I am so glad I found this thread - it has been bugging me wondering if my iPhone 6 plus is a defected unit, but it seems this is a common problem.
If I tap on the top left of the screen it makes a clicking sound like it is a little loose. When I look closely at the phone whilst doing it I am unable to see any movement - it looks rigid. It is getting to me because this area of the screen is mostly used for "Back" buttons - so it gets tapped a lot, and it feels different to the rest of the screen and makes an audible click, rather than the soft thud when you tap anywhere else.
If press down on the left hand side of the screen then repeat this and tap on it, it feels and sounds solid, like the rest of the screen. At first I thought it might be because the volume rockers are housed here, but this confirmed to me it is definitely the screen.
I am on the verge of booking in an appointment with apple to replace the unit, is anybody else in the same boat?
iPhone 6 plus 128gb btw.