During the shaving routine with the balloons at the beginning of the film, the amount of shaving cream on Costello's face changes between shots.
The number of fish sticking out of Lou's coat collar changes about halfway through the scene in the diner, indicating at least two different "takes" were spliced together.
When Abercrombie (actually, Lou Costello's obvious stunt double) pulls himself up on the "DON'T STAND UP!" sign on the roller coaster, part of his head disappears when the roller coaster cars pass beneath in a special effects shot.
When Lou is sitting with the fake beard on and he puts the turban on his lap, the man next to him pours milk into the turban but it splashes all over Lou's hand. Lou then places the turban back on his head as if he didn't know it was full of milk.
When Bud plays the record to get Lou to sleep, Bud lights a cigarette lighter in the darkened room so he can read the paper. The studio spotlight flicks on a little too early to be the light from the flame.
When Costello reveals he has a fake beard on, he runs out of the restaurant and flips over a chair. the bottom of the chair says "3A", referring to the prop number.
During Costello's shaving scene, members of the crew can be heard laughing off-camera.
When Abercrombie is posing like a puppet in the western film, he is taken to the second floor of the room on stairs, a string attachment is visible that holds the doll that replaces the actor.