I have same screen issue on my white 64gb iphone 6. The lower right corner of the screen was loose and made a clicking sound. All the other corners are solid. The clicking happens intermittently, but still was almost everyday. I made an appointment at my Genius Bar, about 15 miles away, but the clicking wasn't happening at that particular moment, and the store was so loud you wouldn't hear it anyway. He implied he couldn't do anything unless he could reproduce the problem. He said that a slight amount of looseness is with tolerance "within specs" for apple. He said it could be looser in the cold and it needs some extra space to account for expansion in the heat. He didn't seem to want to exchange it and I didnt suggest it either. He took down my serial number and took it to the back and opened it up to look at it. He brought it back out and said the screws were loose at the bottom and he tightened both screws at the bottom. It seems ok now and hasn't made any clicking or looseness since then, but it's only been a few hours.
I will see if the problem returns and bring it back if it gets worse. He said it is still under hardware warranty until next September.
BTW, I had the same issue with my black iPhone 5 two years ago, except i could reproduce the problem in the store and they couldn't fix it and they agreed to exchange it, but they seemed reluctant. The second unit was perfect.