tl;dr: My left AirPod had some hardware issue. I got a new one. Now the AirPods work great.
The morning Apple's AirPods went up for sale, I was boarding a plane, and had just gotten to my seat on the plane. I knew they'd be in short supply (though I didn't know just how short—my local Apple Store only gets a small batch every week, and they're sold out in hours!), so I quickly ordered a pair, then set my iPhone in airplane mode for takeoff.
These things are awesome... though a little pricey.