Okay, in the absence of advice about my annoying artifacts - I’ve cleared them by myself!
First : the glass and liquid were not "set smooth"ed - so I was getting some artifacts from the subsurf faces
Second : there were some coincident surfaces between the glass and the liquid, causing some more artifacts.
In fixing these, I discovered further artifacts due to the fact that the base mesh for the liquid did not have sufficient faces on the surface.
I’ve now added some basic cubes for additional reflection/refraction visibility.
The blend is here: