The reflective part of a mirror is behind the glass, so the thickness is realy irrelevant. There is a point in the fact the mirrors are not curved so some misalignment would result. It seems to work well enough though.
Actually, if he's using rear surface mirrors, then the thickness is more important.
Most glass reflects about 5% off each surface, so the energy from the front surface of the glass is not being directed at the same point as that from the read surface - it's off by the thickness of the glass. (actually, it'll be the thickness of the glass times the sine of the angle of incidence, I think)
Additionally, some of the energy gets absorbed by the glass, and the thicker it is, the more energy is absorbed.
Neither of those effects is particularly huge, but they are dependent on the thickness of the glass. Both effects are eliminated by using front surface mirrors instead.