No body in the Solar System is round. I assume that
you'd have to go by some sort of percentage deviation
from a iso-potential surface.

Perhaps he meant "roundish"?

Just off the top of my head, we'd add: Earth's Moon,
Io, Europa, Ganymede, Callisto, Titan, Titania, Triton,
and Charon. If we take it all the way down to Ceres'
size / sphericity it'll be a mess. The big question is,
where's the dividing line and WHY?

Maybe I was just reading between the lines, but I got the impression
that he was going on the principal that planets orbit a star and moons
orbit a planet which orbits said star. That would leave out all of the
moons that you listed.

Since you seem violently against such criteria, what would you suggest
as a criteria for determining whether an object is a planet?