As for what it is I'm looking for in sound? Glance down at my signature. That right there spells out [I would like to think] quite clearly what it is I'm looking for with regards to reproduced sound.
I guess this is where it
does get difficult, because the key word in there is "accurate". If the recording was heavily manipulated, which Adele's was, as the piece by the mixer points out, then
accurate replay, as Tim would say, will give you back exactly what was encoded. Which you may not like very much, but it was a decision by the artist, the producer and company, etc. I am now not quite sure what you mean by "real" sound, unless that is what you would have experienced had you been listening in the same space as the performer, and not through "perfect" monitors or headphones in the recording studio.
Man, I hate to say this....it depends on the recording. Some folks can pull this off and it can sound great. Others, IME, not so much. The differentiating factors are or could be seemingly infinitely variable and would still be subject to listener preference. Simply put, even rather bad or unpleasant sounds [whether synthetic or real] can sound great on a well recorded piece.
One more thought. You mentioned distortion. It could be said that between the original tape/performance and the end result of Adele's CD was nothing short of "distortion" [complete butchering] from the original. Albeit a different application of the word "distortion".
Still seems to come down to good ol' preferences, such a hard thing to grab hold of! And again, there are the words "a well recorded" piece: is it purely subjective; minimal manipulation; capturing of high levels of ambience, real or artificial? A hard one ...?
But, then you say, with Adele, it
was all that manipulation in the mixing. Which Tim would say,
is a crucial component of the recording, that's what was intended. And if all the musicians were completely disparately recorded, then there was never an original, valid recording anyway -- there never was an original performance, just purely a particular version of an assembly of sounds, which suits some people and not others.
Maybe, down the track, what can occur is to have the raw feeds of all the mics available online, 24 or however many tracks, people can then do their own, customised mixes, totally unique to themselves. Then there most certainly will no longer be a "true" recording; it's whatever you want ...
Frank