I'm coming from a 5 and the first 6 I received in the mail from Verizon had a pre-click when you would barely touch the button as if it was popping back into position or the button was slightly misshapen and rubbing against the metal ring. It was driving me crazy so I went to the Apple store yesterday and all the phones on display as well as the two replacements they brought out to me had that very distinct and audible click when releasing the button. I don't like it but as it's been previously stated, it's the new normal. It's two separate pieces of material your finger/thumb is touching now so there is some very slight movement between the two but if it's really loose I'd say take it back. The only way to somewhat silence the new home button is to push toward the outer edge instead of the center.
I also got AppleCare+ yesterday, I've got a feeling it's going to come in handy someday...