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.
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?