Continuity mistake: On the marquee that advertises the show "Band Wagon", the name of the actress is listed as Gabrielle "Girard", but when the scene switches to a shot of someone holding the program for the show, her name on several pages of the program is spelled Gabirelle "Gerard".
Visible crew/equipment: When Fred Astaire is dancing in the train station, there is one shot as the camera pulls back where you can see the equipment/crew shadow on one of the public machines there.