I am also facing the same issue.
I bought 2 new iphone 6 16gb(both purchased on same day).
one of them is working fine,
but on other device I am having the issue of loose display panel.
I went to apple service center but they said they will not replace my phone because its not a hardware issue, they can only repair it.
SERIOUSLY APPLE???
YOUR PEOPLE THINK THAT A LOOSE DISPLAY PANEL IS NOT A HARDWARE ISSUE???????
EVEN A 10 YEAR OLD CHILD CAN TELL YOU THAT ITS A HARDWARE ISSUE.
I posted a video here https://youtu.be/aEkyZb86KRc
Can anybody tell me how to get a replacement
and where to file complaint against that service center??