When Astaire, Wynn, and Skelton are talking about the play never being produced, there are several pictures of M.G.M. stars on the wall. First, from left to right, is Judy Garland, then Spencer Tracy, then Katharine Hepburn, and another I could not identify. The time period in the movie was at that point during the mid 1930s, but those photos were all from the late 1940s.
Most of the movie is set in the Twenties but the fashions and interiors are late Forties. And who knows how the film managed it, but Debbie Reynolds, in her number impersonating Helen Kane (the boop-boop-a-doop girl) is dressed exactly like Jackie Kennedy in the early Sixties--pale pink suit, pearls, white gloves, and little hat on the back of the head.
When Harry hurts his hand playing baseball with the Washington Senators, his glove is knocked off of his left hand and he holds the index finger on that hand in obvious pain. Immediately afterward, when he is having difficulty playing the piano because of his injury, he has a bandage on his right index finger.
When Astaire and Ellen are dancing to the Husband and Wife dance number, they toss everything off the kitchen table. The toaster is pushed off the back of the table onto the floor. In the next instant, it has disappeared from view.