The "A Pretty Girl is Like a Melody" number incorporates snippets of Gershwin's "Rhapsody in Blue", which was premiered circa 1924, but after its performance Anna Held, who died in 1918, is still portrayed as alive and married to Ziegfeld.
In the "Rhapsody in Blue" portion of the mammoth "Pretty Girl" number, one of the silver-fringe-and-antlers quartet of dancers gets visibly disoriented when her group does its final moves. She's the second one from the left, and her movements are completely out of sync with the other three until, with a thump, she sits down on the stairs. Since the incredibly complex number was shot in very long takes, the error was allowed to remain in the film.
During the circus number, each dog moves forward into a box painted on the floor of the stage. The second dog from the right moves forward out of the box, then is seen back in the box in the next shot.
In the early part of the "A Pretty Girl is Like a Melody" number, there are girls pretending to play a Japanese Shamisen with mirrored fronts. Just before the middle one goes out of frame, you can see a sign being held by a crewman, likely to give instructions as the shot progressed.
In the musical number 'You' one of the hopping chorus members (second from the front) does not land both her feet squarely on the bed. The right foot falls short of it altogether and strikes the floor. Fortunately for her, the downstage dancer all but obscures the misstep. Nonetheless, to this hoofer's credit, she may have missed the bed, but like a trouper, she doesn't miss a beat.