The Walt Disney characters are seen getting their costume heads prior to the parade. When the characters are seen on parade inside the tent, they are in different costumes to what they were wearing when they got the heads.
In one scene Buttons the clown is wrapping cloth tape around Holly's trapeze bar. He wraps it for about a third of its length then lays it down. When he lays it down it is clear that there is almost no tape left on the roll. When he picks it back up a short time later the bar is wrapped almost three quarters of the way and the roll of tape is much bigger.
When the view from the cab of the second section train is shown approaching the rear of the first section, the first section is parked on a right hand curve in the tracks. However, when the second section is shown colliding with the first section from the viewpoint of the middle of the first section as well as in some previous shots, it is obvious that the first section is parked on a left hand curve.
Buttons spends several minutes wrapping a trapeze bar with tape before following Holly into the ring. When they return the bar has no tape on it.
When Klaus is seen waving to stop the second section as the engine speeds towards him, the right Cylinder on the Locomotive are discharging steam. When Klaus' car is hit by the locomotive, there is no steam in sight. As a side note, the left Cylinder cock is not discharging steam, in fact both would very quickly alternate on and off.
When Brad is checking the baby gorillas after learning they may have contracted the mumps, a crowd of onlookers is gathered right behind, plainly staring at the camera filming the scene.
During a brief long-shot of the Grand Parade, you can briefly see Cecil B. DeMille's camera unit at the bottom left-hand portion of the screen in a corner of the Hippodrome where the parade takes a turn around the ring, with DeMille himself standing next to the camera.
When Mickey Mouse and other Walt Disney characters walk around the ring, the band plays the song "It's A Hap-Hap-Happy Day" from Gulliver's Travels (1939), which was released by Paramount, not Disney.
Brad constantly refers to all of the elephants as "bulls" even the female elephant Ruth. He's using the term incorrectly. Only male elephants are bulls. Females are called cows.