Stereo soundstage:
Width
Height
Depth
3-dimensionality
Does instruments and voices stand alone on a black, silent background?

Balanced frequenzy range:
Natural midtones
Good solid bass
Airy, natural treble

Details:
Crispy sound
"Timbre"
Natural sound and size to voices and instruments
Natural dying out of sounds, not too abrupt
Air over voices, brass, flutes, wind, (stroken) strings
Overtones are crucial to create a natural sound. Do you hear them?
Do you hear the woodwork on a piano? On a harp? On a violin or a guitar?
Can you tell the difference from nylon vs metal strings?
Do you recognize a Fender and a Gibson guitar?
Does a standing bass vibrate like it does IRL?
Does a church organ sound like you remember?
Does applauses sound like peas falling on a tin roof?

Dynamics:
Speed. Are drums, bass, string attacks, brass fast?
Does a classical orchestra sound natural? They have a lot of dynamics.

Stress, distortion and musicality:
Does the music tire you out?
Can you keep the foot still?
Do you want to just go on and on listening through your records?

Please feel free to add...