[danans]

> But I've never seen a damp rag be shiny in any direction.

The surface of a cloth is still much less smooth than a polished car, cd, etc, so is it possible that the specular reflection happens, but at a contrast that is too low for our eyes to detect, or in enough disjoint sections that we can't perceive it as a single effect?

There are plenty of phenomena that fall out of the range of our unaided perception.

We would, however, probably observe the specular reflection of instead of water we used a thicker transparent liquid, like clear glue.