What this sounds like to me, is I’m picturing an old/cheap acoustic guitar, maybe a mandolin or something – either not very well setup or otherwise kinda difficult to play…remember your first cheapo acoustic with really high action that hurt the hell out of your hands? The sort of “plinky” timbre, it’s definitely not in tune at least on certain notes or intervals, the sloppiness of the playing in general (I mean, there are at least a couple of botched notes – at 2:09, and at 2:16 the sloppy slide; more plunks in the second solo), all of it telegraphs to me deliberate imperfection. On a well-tuned and intonated instrument that part would sound as slick as the rest of the production, but it does give it a standout character because it doesn’t.
There’s definitely a delay on it, but the instrument itself is indeed a little out of tune and sort of sloppy-sounding. Either kind of a crappy instrument (wouldn’t be the first time a pro used one to achieve a particular sound) or a deliberately relaxed/sloppy take. I don’t think there’s anything more to it than that.