How do you know what you're missing?

@cat_doorman, you have posed the question I’ve asked myself over the course of the past 15 years or so since I’ve gotten back into my two channel system. 
The dragon I’ve been chasing is the sound I heard, 16 or 17 years ago at the beginning of my serious audio journey, of a high end set up in an audio shop that seemed to me a completely transparent, three dimensional, gorgeous and mesmerizing presentation. I have no recollection of what any of the gear was, but as I was listening to it, I thought, oh my gosh I never knew a stereo could sound like this, this is what I want.

After that experience I simply picked an element, one at a time, in my system and made a change. When I upgraded my speakers it made a big improvement, when I upgraded my cartridge it made an improvement, when I upgraded my turntable it made an improvement, when I upgraded my CD player it made an improvement, when I went from a solid-state integrated to a tube preamp with a side of the road solid-state amplifier it made a big improvement, when I replaced that solid-state amp with a tube amp it made an enormous improvement. All of this has taken place over the course of 15 or 16 years which has allowed me to afford the changes I’ve made in my system and appreciate each change as I made it.
Live music is always a good experience, and as everyone says, venues play an enormous roll in the quality of the sound. My wife and I have been fortunate enough to have attended quite a few concerts at Disney Hall in Los Angeles over the past several years. Disney Hall’s acoustics are exquisite. Whenever I am in there, I think to myself, this is what I want my stereo to sound like; open, effortless, shimmering, satisfying. 

I found Jim Smith’s book, How to Get Better Sound, very helpful. His main point is to work with your room and the equipment that you have in order to optimize the quality of the presentation and maximize the enjoyment you get out of your system.

if you are fortunate enough to live nearby a brick and mortar audio shop, establishing a relationship with them can be very helpful in this pursuit. Of course that relationship does presume that at some point you are actually going to spend your money to buy some gear from them. In my case, I’ve been working with a particular shop for the past several years and because they know me as a legitimate customer they have been very generous in allowing me to demo gear I’ve been interested in in my home. Some of the gear includes two different amplifiers, a Bluesound Vault and a Chord Qutest dac. I did end up buying one of the amplifiers, the vault, and the dac. I was in the market for all three, but it was so valuable to be able to hear them in my living room.

If you have a friend who is also into this hobby, that can be a great opportunity to hear another system in another real room. As a matter fact I have a friend who is willing to lend me his pair of Harbeth Super HL 5+ speakers to set up in my room while he’s out of town for a couple of weeks. 

And in answer to your last question, what if I’m not even aware that a problem is a problem? I’d say that I was absolutely astounded at how big a difference a high-quality amplifier made in the overall presentation of my system. So in other words, now I am completely aware that everything relates to everything else and everything sounds.

My apologies for the long self-indulgent ramble, but it’s a Friday afternoon, and I have a little time on my hands. Thanks for your patience, and enjoy the music, I know that’s what I’m going to do this weekend!

You have to hear it in your won system  usually having a network where you can each come to the others home with a piece of gear or borrow from a local dealer  Many cable companies all ow you a trial period - musical direct has a trail period

But you don't know what you are missing until you hear it in your own system.

Happy Listening

It's a great question!  Much of the answer depends upon what type of person are you.  If you just want to listen to music and enjoy the experience you won't really worry about how it could be even better.  The music sounds good and you're happy.  For that type of person your question is not particularly important.  There's another type of listener who is more interested in what they call "the journey".  No matter what their system sounds like, they are always thinking about the next step.  It's axiomatic that their system can always be improved.  I suspect they do like listening to music, but they really like listening to their systems.

Once you figure out what type of listener you are the answer to your question is kind of self-evident.  If you're not

Years ago ( mid nineties) when l was in the process of trying to improve my stereo system l had a chance to hear a pair of lnfinity RS lll speakers! Holy ****! they were amazing! The song that was playing was Rodger Millers King of the road. Talk about a bench mark! Another speaker that really impressed me back then was the Infinity Kappa 9's Of course I could never effort either pair back then, but by listening to those speakers it really helped me in my journey to put together a somewhat modest but very enjoyable system that l think has some of the hi fidelity traits of those great speakers

onhwy61 expresses well what one goes through 'getting there', as do the other responders.  What everyone hedges around is the old conudrum:

Age & Experience. (*groan*....'oh, No, not That again....')

What you heard when/where/how/with whom (or not)...what it sounded like that impressed, how it made the back of the neck hair respond (or whatever else occurred)....

The 'I want That daily in my life on demand' kinda thing...*s*

Then the hat trick is to Find and Keep 'That'...because once the stone is rolling it gets harder to Stop and say 'enough'. ;)

Carry a couple of cd's and/or some fav's on your phone with the appropo IC....shop around....consider what you like about the music you play and what it is that you enjoy about it....

What would seem to make it better; more discrete, dynamic, quiet in the quiet passages, nimble in the complications....

...and keep in mind the space listened within can play as big a role as the equipment...and you as well.

Only you will know the answer(s) to all of the above.

And remember:  All of us have the same equation to solve.

Good luck, and have a good time at it....which IS the point, after all...;)