In one song by Dutch-Swedish singer/songwriter Cornelis Vreeswijk he suddenly realises that he has started to sing a verse a second time, so he ad-libs “I sang the wrong verse but I hope you don’t mind. I can sing the next verse twice, if you want me to”.
At 3:33 in Guitars In The Sky by The Records, there’s a (?) squeak. It doesn’t detract from the solo or the song.
At about 3:35 of this version of Steve Miller’s Space Cowboythere’s something a little odd followed by a bit of a giggle. This is not The Joker, it came about a year before that.
Don’t know if studio mix flubs count, but on Matilda Mother by Pink Floyd, there’s an obvious edit before the final verse where the producers obviously just abruptly cut from one mix to another. Syd probably didn’t care but the rest of the band should have.
as far as the OP’s “Famous is better” criteria, a similar phenomenon occurs in Beck’s “Loser” in the verse beginning “forces of evil and a bozo nightmare” but there’s 50 50 odds that Beck did it on purpose rather than not caring like Syd or just plain missing it.
"Trains to Brazil by The Guillemots has verse where the singer starts but then trails off…it’s unsettling and awkward to me.
I swear there’s a Radiohead song with a false start, but I’m drawing a blank now.