It would have to be something from 1965, when they hit the burnout wall for a quick minute due to all the touring and stuff. Probably something from BEATLES FOR SALE. I think their cover of "Kansas City" is pretty ephemeral, although it might have been better served by having been recorded a few years earlier.
"Hello Goodbye", eh? Goofy, yes, but I still get drawn in by the production/engineering job on that one, how truly FAT all the stringed instruments (guitars, bass, and cellos) sound and how the drum sound is like you're inside the drum (which may very well have been how it was miked, I dunno). And if you were buying 45s back then (and I was), it's a good chance that you played the B-side of this one more than the A. A little ditty called "I Am The Walrus" (and with a different mix that on the MMT album at that!) it was...
When it comes to Pop, good/clever/innovative/whatever production can render a song's relative "merit" irrelevant as far as I'm concerned, and I can't think of too many Beatre songs outside of the period mentioned above where this is not the case for me. They weren't all great songs, but they were, for the most part, all great RECORDS.
In Pop, the rules are different...