I actually like the tune itself very much and Mark's tipsy singing doesn't bother me at all. My problem with it is that it sounds like a poorly recorded pub performance. I didn't expect anything fancy with long solos or anything like that, just a nice and warm song performed by two legendary musicians and a little band - and a metronome lol can anybody else hear the little, let's say, mistakes that I hear?
Maybe I am reading too much into it, but couldn't what some perceive as "poorly recorded", "little mistakes" or "first take" be done intentionally by the BG perfectionist to correspond with the one they sing about and that needs more than just beauty sleep?
A couple of things to consider: it's Mark and Tommy literally playing together for the first time (on record) and with Mark being not a monster virtuoso jazz giant with whom Tommy usually plays, it's going to be a slightly rough performance already, which goes along the song well anyway and maybe because of that Mark thought about this song to play in the first place.
Second, is that of course this song is on Tommy's album and it completely changes all in terms of the sound, because Tommy's the boss in this situation. Mark and anyone else in his studio can have their opinion, but hey, it's Tommy's record!
To be honest for this reason I don't like Tommy & Chet duet album, because the sound is too... Cocktail, too lounge and laid-back. Mark & Chet duo album, in the other hand, has a very good sound. So maybe Mark had some impact on the overall sound, but anyway, the new song sounds like one take, because these two love to brag about recording anything with the first take