Opening the hinge made various creeky and popping sounds. I surmised the worrying sounds were caused by internal misalignments or cracks, which might have been caused when I flexed the body of the Air in a (very stupid) attempt to level it out.
Removed the bottom plate, tightened up some internal screws, marveled at the internal engineering masterpiece that is the Air. There was indeed a tiny crack in the rim of one of the mounting holes for the battery; no big deal. After resetting the bottom, the sounds were gone.
Use care when unscrewing the pentalobe screws that secure the bottom plate. They appear to strip easily. Because of the concavity of the bottom plate, you have to unscrew at a bit of an angle.