Beej, yes nice thread, I'm enjoying this one myself.
I think a lot of it boils down to the Turntable, and design. What works with a Sota with a Vacuum system, won't work for another, VPI Styled Clamp maybe won't work on a Thorens, etc. Platter design is one aspect.
But I am a firm believer, that if some form of clamp, or weight can somehow make a slightly warped-dished record lie flatter, that this will be a clear advantage.
The less trouble a Stylus has to go through to traverse through the groove, the better.
That Stylus riding up, and down vertically can usually be quite clearly heard through the speakers.
I can remember the old days, with the Shure V-15 on my now long gone Pioneer PL-51 Table, with that whoosing sound coming, and going everytime that cartridge bobbed up and down on a less than totally flat record. That overall sound became much more stable when I then switched to a VPI Table with the clamping system.
That all those little anomalies do add up. A little noise here, a little hum there, a dirty stylus here, a warped record there, they all were cumilative combining to make a slightly less than stellar sound.