And that's why I'm successful at dissecting tracks!
I think most players have forgotten, or are too young to have experienced how many blatant musical/lyrical/production mistakes were released to radio in the not too distant past. Timing issues, lyric flubs, arrangement flubs (someone came in at the wrong place...), tuning, bad punches & edits, etc etc. But we accepted those things because as listeners, we weren't over-educated about performance and production and what to expect from a track or a band. Players and producers and labels were only slightly ahead of us, since they went ahead and released those recordings anyway!
I don't think the track in question is so egregious, it's that so many of us have come to demand perfection. Funny, many of the same people decry the use of clicks & sequences. And artists and producers have generally risen to meet the demand that they basically created when they got better at what they did. It's gotten to the point where even the slighest variance can spark a discussion like this.
In my mind, a song or track either makes me feel good, or it doesn't. In this case, I just don't happen to like the track, but it has nothing to do with the organic nature of it at times. Playing it 'correctly' wouldn't improve it.
As for listening to the old songs - and still some new ones - with anomalies, I 'hear' them, but they're not really a big deal. I don't sit around pondering how those groups managed to be popular, and in some cases, still endure. It was what it was.
A classic example is Miles Davis's "Kind of Blue"; An engineer had mistakenly set the tape at a very slight slower speed, this ended up giving the album a ethereal kind of feel. Some elitist jazz critics knocked him for releasing it that way. You can actually buy the corrected version on a specially released CD, I'm a vinyl listener so I won't need to do that. Same thing happened with the Doobie Brothers "Black Water, the engineer hit a mute button of sorts and the result was the Acapulco chorus, now famous. Mistakes in the studio can be fortuitous.