Before Charlie and Vinnie leave, Peg claims Charlie stole her watch. Although Charlie briefly grabs her wrist, throughout the scene she is not wearing a watch.
As Peg calls out to Charlie before he leaves, he is holding his cigar in his right hand. When the camera cuts back to Charlie he's now holding the cigar in his left hand and the stolen watch in his right.
The record store worker says he doesn't know the song when Al hums it to him yet the song was on the store's jukebox. Surely the worker would have heard the song at some point.
Al says he called the radio station to ask the DJ the name of the song that is haunting him. He ends the story by mentioning that the obviously insane DJ lit up a banana like a cigarette before hanging up. How exactly would Al know he did this over the phone when he couldn't see him?