What exactly is critical listening? Who does it?

Critical listening and enjoyment listening modes are not mutually exclusive

I should have added they can both occur simultaneously. Listening is a skill, one that can be improved through mindfulness and practice, judgement is where we go wrong, free your mind and your soul will follow. 

I am happily at a place where I am satisfied with my components and vibration control and non-equipment issues like speaker placement only needing to make any decisions except when something breaks or wears out. My cartridge will be 5 years old next month and I listen about 750-1000 hours a year so it should wear out soon. Then I'll have a decision whether to buy a replacement, get the stylus replaced (and anything else that needs bringing back to specs) or possibly upgrade. So whenever I listen closely, it usually is specifically to an album that is one of my favorites, or if I have gotten a better pressing of one of my records.

The best times are when I am not listening closely and notice something I never heard before or if it sounds better  than expected. When it sounds worse it's a bummer.

I know it can always sound better with a better component, but the incremental improvement as this point is not something I want to invest the time or $$ in.