I knew that there were some pretty serious disadvantages to using this material, and those turned out to be even more serious than I'd thought. The only real advantage is cost. I was able to make my handheld concave mirror for less than $5, and this video by Dan Rojas demonstrates that it's possible to build a concave mirror more than a meter in diameter for less than $25. His method involves stretching the mylar across a frame then applying suction to make it concave.
Caution: do not try this at home. Fire hazard, blinding hazard. This isn't just boilerplate. The blinding hazard turned out to be quite a bit worse than I'd expected, and I had thought I was already being a bit paranoid. I would strongly recommend against copying the techniques I've used here; what I was doing was quick and crude, intended only to get a sense of how the material behaves.