What exactly is critical listening? Who does it?

Maybe it’s like going to a museum and looking at a painting done by a master. For many just visually looking at it, it achieves lots of enjoyment. And then for others, they understand all the work related to color choices, brushing techniques, contrasting, depth perception - they put a lot of thought in looking at the Picture because they understand what it’s all about.  Most mere mortals have no clue.

Many of us mere mortals may wish we better understood all that goes into the picture which no doubt would allow a better appreciation for all it took to achieve it.

There are some remarkable paintings in this world and I wish I would’ve taken some art classes in college. 

There are different types of "critical listening" for different purposes. In audiophile land, I think it is often meant to describe listening for shortcomings in the presentation of a system or given component. But it can also involve listening to compare different pressings of the same record, to evaluate their respective merits. In musicology, there are also different types of critical listening- one might be to analyze motifs or how it fits into the overall body of that composer's work, its influences, historical context, etc. Forensic musicology often involves picking out allegedly infringing phrases or elements and finding historical precedent for their common usage as building blocks by other authors. I think you need to provide context to afford more meaning to the term. To me, I most often associate it in home audio reproduction with listening to where a system or component reveals its shortcomings. 

Correct.  Get busy now and let us know your findings. Chop chop!  Enjoyment is right out! 😉

Myself:  guilty as charged.  Call me Mr. Critical.  Just be nice about it.  Not too critical, please.  

Correct, critical doesn't necessarily involve judgement. I mentioned in another thread how in recent years more focus on qualities of the recording itself. Producers/engineers play a major role in bringing us these works of arts, I've learned to turn off the judgment cap, just let the recording come to me, much more satisfying listening sessions with this. You still the warts, they become curiosities rather than irritants. 

"critical doesn't necessarily involve judgement."

Correct:

Critical