Plot hole: In "Violent Is The Word For Curly" (1938), the stooges start singing "Swinging The Alphabet." After Moe starts, he has the girl students join in on the song. Some mistakes follow - first, after a few letters are sung, ALL the girls together change to a higher note and faster tempo (which is impossible since NONE of them knew this song before - let alone ALL switch notes together). Also, they all sing "LA LA LA" backgrounds suddenly when Curly sings solo again ALL at the same time.
Plot hole: In the episode "Scheming Schemers" (1956 - fake Shemp episode) at the start of the episode, Moe is given the address for a plumbing job over the phone and he and Larry take off in their jeep - accidentally leaving Shemp behind. Next scene, Moe and Larry are in the house working on their plumbing job and minutes later Shemp just shows up outside in a separate vehicle. Shemp would not have known where the job is since he was left behind and never would have known the address Moe and Larry went to.