Read this post, you may have gotten one with the troublesome Nand.
http://forums.imore.com/iphone-6/312065-mlc-tlc-nand.html
I would have to jailbreak to even find that out, wouldn't I?
The thing is I don't know if this touch responsiveness issue is hardware or software related. Hardware related, I would need to go to the Apple Store and get it replaced. If it's software, then the only thing I can do is hope they fix it in a firmware update. I don't even know if the genius bar can confirm the issue or not to do anything.