I've spent the better part of 4 hours trying to figure out how to fix this (also taking apart an xbox S-controller to look at the differences) and the fix isn't sanding alone. I'm pleased to say I've managed to make the d-pad tight as hell and it's improved my Tetris game considerably.
First things first, why it's not so hot: MS indadvertantly made two small changes from the old Xbox S-controller. 1: The distance between the button membrane (plyable plastic bit that hits the contacts on the circuit board) and the bottom of the d-pad's contact points seems to have shrunk very slightly (2mm?) so the pad can slide back and forth without pressing any buttons. Bad! 2: To fix this MS made the wall around the D-button thicker (just look at it).
These two problems come together in the following way: Sometimes, when you press a direction you can't get the membrane to connect because there isn't enough room in the well. This is where sanding comes in. You sand all the way around the outer part of the well so the d-pad can be moved enough to make contact but you're not done yet. But now the d-pad will slide around even more which is bad.
All we're going to do is add a very thin layer between the membrane and the bottom of the plastic of the d-pad to fill that space.
The end result is a directional pad that feels really snappy. I was surprised when I was finished with the first one how the controller actually clicks when you press in the direction you want. It feels completely different and 100% better.
(I originally posted this at cheapassgamer.com)