Il Mio Problema
A user at the company was complaining that her trackpad would constantly think she was clicking and holding to drag things, even when she wasn't. I tested it and confirmed this was, indeed, an issue.
La Mia Riparazione
After first looking around at potential software fixes (firmware updates and the like), I proceeded to open it up. No signs of water damage, no battery swelling from overcharging, no noticeable debris. I took the trackpad out and stuck it in another MacBook Air; same problem. Ordered a replacement part, installed it and all is good to go. Still no idea what crapped out on the trackpad in the first place.
Il Mio Consiglio
Be prepared for options. There are a bunch of things that could impact trackpad usability, but not all of them require a replacement part.