When Rufus is singing near the beginning of the movie, he sings to Gloria then turns around to sing to another person but instead he faces a curtain. Without missing a beat, he sings to it then has to take a big step to get back to where he's supposed to be going next in the choreography.
After Ambassador Trentino has announced, he steps down the stairs followed by two gentlemen and crosses two ladies before he kisses Mrs. Teasdale's hand. Next shot the two ladies are just behind him yet and the last man after him is already on Mrs. Teasdale right hand-hand side, giving his back to the wall.
When they meet, Mrs. Teasdale holds Firefly's right hand while he holds the cigar with his left hand. The subsequent shot shows him holding the cigar with the right hand and the deck with the left one.
During the fight with the lemonade vendor, the vendor gets squirted with lemonade and his shirt gets soaked. Seconds after, while the vendor is tussling with Chico again, we see that the vendor's shirt is completely dry.
When Firefly arrives at his reception, he is wearing a dark swallowtail coat. Then after Mrs. Teasdale greets him, we go to a two shot, and Firefly is now wearing a lighter shade jacket with dark piping and a glove in the breast pocket. When Ambassador Trentino enters, Firefly is again wearing the swallowtail coat, which he retains until the very last shot of that scene, when he is again wearing the lighter jacket, without the glove in the pocket.
In the mirror scene the reflection, which is Pinky, holds a black top hat behind him (you can see it from the side shot) and Firefly (with his back to the camera) holds a white hat behind him. You can clearly see the black top hat as they do the pivoting around one another. When they put the hats on, the reflection, (Pinky's), hat has magically turned into a white hat. Then after they take the hats off, in the next scene, the reflection, Pinky's, hat turns back to the original black top hat.
The removed horseshoes that we see lying on the floor (from the horse that Pinky was riding) are not actual horseshoes but the type that are used in the game of horseshoes. They are much larger than regular horseshoes.