When Stuffy gets on the horse with the wagon, he is wearing a coat and dark trousers. As jockey he wears white pants and jockey shirt. While he could have lost the coat easy enough, there was no opportunity for him to change pants.
When the horses head to the track, the announcer notes only eleven horses are headed to the track and that the added horse, Hi Hat, is nowhere to be seen. However, when the board was shown with the horses listed, twelve horses were initially listed for the race with two scratched and then Hi Hat added, so if Hi Hat wasn't heading to the track, there should have only been ten horses.
In the closing seconds, Hackenbush takes off his hat and puts it up on the tip of his umbrella. When the camera angle changes to a wide shot, he does it again.
When Tony starts playing, "Steinway and Sons" can be seen on the piano. In later shots, the logo is missing. This is because it has been swapped for a prop piano that is destroyed by Stuffy.
While Chico is playing the piano, at certain angles, the row of hammers can be seen bobbing up and down, because he's using the pedal, but they actually aren't striking the strings, proving the piano is non-functional.
During the water festival, in one closeup, Gil's boat rotates but comes to a very sudden stop, instead of slowing in its turn first, showing it wasn't actually on the water at the time.
During the water festival, Gil's singing is often unsynchronised with his lip movements.