I have a CD of Leonard Bernstein conducting Appalachian Spring with the LA Philharmonic. I played it a few months ago for the first time in years (also for the first time since making several significant upgrades to my system). I had pulled it out and put it on just because I wanted to hear Appalachian Spring, paying no attention to who the conductor was. Several times during the quiet section within the first few minutes of the piece I heard a soft human voice grunting, or saying a quiet "uhnn." As soon as I heard it, my mind said, "that's Bernstein." I knew his voice because I've watched videos of him in rehearsal. It was absolutely crystal clear and obvious in my current system, but I don't recall ever noticing it during the many times I played this CD in years past. Now that I know it's there, I can discern it listening to a YouTube recording, but it doesn't stand out, and I certainly wouldn't have identified the grunter listening to it that way. Like the OP said, not really a critical test of a system, but kind of fun!
What to listen for?
This is aside to the obvious ones such as does a piano sound like a piano, the singer's voice sound close to them live, etc.
So, what I am trying to put together a list of songs where there is something specific to listen for. For instance, in the song Guinevere (CS&N) I have read that Crosby should sound as if he's standing in your room, front and center. On the acoustic Hot Tuna Album, they are playing in a bar and a beer bottle breaks landing on the floor - it should be sharp and sound like it's in the room with you. On Babylon Sisters there are some cymbal crashes on the left that should be crisp and not smeared. On a Beatles song (I forget which), a chair squeaks and a door opens and closes in the studio.
A good system will revel these little things. Any other that you have heard of?