Glad to hear that both your phones are working, but I'd be cautious re: the slanted power button.
I originally paid for 3 Droid Turbo 2's at Verizon, got redemption codes, and ordered the phones via the Motomaker site. All 3 arrived about 8 days later. Two were fine, and within 24 hours one kept randomly shutting off, despite being fully charged. We tried pretty much everything - uninstalled apps, wiped cache, factory reset. It was truly appearing to be a hardware issue of some sort, and it got progressively worse day by day after it first starting happening, and finally it became impossible to get the phone to start up again.
I examined the bad phone and compared it to the two working phones. The only visible difference was what the OP described: the power button on the dead Turbo 2 was slanted: the top was normally extended, but the bottom of the button was somewhat collapsed into the phone. With the other, working phones, the button extends straight out from the side of the phone -- top and bottom equally extended, and the button remains properly perpendicular to the phone as I press it in to turn the phone on/off.
I had to call Motorola customer service, was given a new redemption code, and had them build a replacement while I returned the dead phone. The new one arrived -- works perfectly -- and its power button is just like the other two working Turbo 2's: no slant to the power button at all.
In our case, I'm convinced that the power button was the source of the problem. No guarantee that a slanted power button means trouble, but if you find that on/off functions start becoming the least bit unusual or hesitant, I'd strongly consider looking for a replacement.
Jon