What to listen for?

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!

I gauge sound quality using three song sections.  1st=the bass guitar, drum snap and cymbals, and guitar highs and distortion at the end of Fleetwood Mac's "The Chain [Alternate Mix] from "25 Years - The Chain" compilation.  2nd=very clear bass rumble at the end of "Enter Sandman" from Metallica.  Also, the boy clearly saying "My soul to Keep".  "Keep" is often unintelligible.  3rd=the clarity and separation of the bar singing at the end of "Friends in Low Places" by Garth Brooks.

Sometimes in order to achieve a natural and balanced presentation I have to give up some of the details I've heard and are aware are being masked now. Hyper detail often comes at the expense of overly harsh and analytical. But yeah,it is exciting when you discover something new- a wrong string pluck that's quickly damped(oops!),a squeaky piano pedal,etc.It feels more real and "human".

The Hot Tuna song with the shattered glass - listen closely and you can hear the glass being swept into a dustpan:-)

if one is thoroughly familiar with live sound [i played in a concert band for over a decade], compare that remembered sound with what the system you are listening to puts out. you are listening for both omissions and commissions [aural sins] in sound. the loud sounds should never "blast" or overwhelm or drive people out of the room. the quiet sounds should be crystal clear without straining. there should be a naturalness and balanced frequency response where there is never any boominess or thinness/shrillness at any time. male voices should never be thick and female voices should never hoot. you should easily be able to notice musical incidental sounds such as feet tapping/shuffling, sheet music turning and music stands creaking, musicians breathing and their clothing rustling. this assumes that such didn't fall beneath the resolution of the original recording equipment. you can hear it in an ordinary audio CD, RCA Red Seal Fritz Reiner/CSO "Scheherazade," even on mediocre equipment. of course the listening room is a major part of all this, you must have absolutely no external noises [HVAC roar, humming from appliances, neighborhood noises] leaking in, better luck with this if you have your man cave in the basement or live in a mansion in a ritzy neighborhood], or else you basically lose the bottom half [below about -30db] of dynamic range in most quality recordings. if you live chockablock with your neighbors, you essentially lose the top 10/20db of your dynamics as well in terms of having it not much louder than background level to avoid disturbing your neighbors. in this regard, a good audio compressor is a good addition to most folks' audio systems as it brings the dynamics in within the limits imposed from within and without the listening room. at least one audio reviewer has mentioned this. 

You will hear fine details that are otherwise not audible on a lesser system.

Bass - How tight or loose the bass is (including but not limited to its style and textural resolve) Can be described as boomy, full-bodied, etc. and of course being able to discern bass extension etc.

Midrange - It should sound like being inside the microphone, capturing the very same tonality and extension as the singer’s voice. Sharp or peaky female vocals should, for example, bloom naturally. Like in Diana Krall's - Black Crow. With other artists, you can almost tell what they ate just before recording etc.

Midrange/instrumentals - being able to establish the relationship between vocals and instrumentals. How prominent or recessed are the instrumentals? Do they ever overpower the vocals; or do they instead act as a perfect backdrop to elevate that performance? Are there fine details that were reproduced slower, rather than faster? This is telling of a resolving audio system.

Treble - Like midrange, it should be extended and bloom naturally. Sharp peaks, dips, and even unpleasant-sounding treble frequencies should coexist organically, with the rest of the spectrum. A cymbal that wasn’t recorded or mixed/mastered properly on a track will sound artificial, papery...not metallic enough and with recessed attack/decay/fade out. )

Brilliance (uppermost treble) - The "air" so to speak in a recording. The space between instruments. The tempeature of the air in a room, which results in a overlay that must coexist with overall tonal balance. Not enough during post-production can result in a track that sounds too "digital" or congested.

Perhaps put together some reference tracks and compare/constrast? I know quite a few that can help...