> It has always bothered me that by "spectrum" they mean not the sort of continuous thing that spectra actually are, but instead some disjoint set of "colors" any one of which might describe a person.

Wasn't Newton making the point that we normally perceive and treat colors as qualitatively different, but that they're in fact caused by a single underlying mechanism that can take on any of a continuous range of quantities?

Thus using the term "spectrum disorder" would be making precisely the same point, to describe a set of apparently qualitatively different disorders that are in fact caused by some underlying mechanism with a range of quantities? (To be clear, I don't know if any so-called spectrum disorders actually meet this criterion, and it's probably more complicated than that, but it seems to be the reason the term was chosen.)