The opening screen says "COPYRIGHT MCMXXXIII" (i.e., 1933), but the closing credits say "COPYRIGHT MCMXXXII" (i.e., 1932).
The establishing shot of Dorothy Brock's hotel door on the night before the big opening shows her to be in room 831, yet when she throws everyone out of her rooms a few minutes later, the door number is 284.
When Denning and Brock are having coffee, there is a cup of toothpicks on the table. However, the orientation of the cup changes from shot to shot.
The same drinking glass (water) is used throughout the movie. The glass is first seen during the rehearsals when Peggy faints. The same glass then pops up again in Pat Denning's home/apartment when he uses it for his lapel flower/button hole, then again the exact same glass appears in Julian Marsh's hotel room, but this time after the company have moved on to Philadelphia.
When Peggy faints and is sitting down near the stage entrance, there initially is a group of people around her. As the crowd drifts away to their tasks, she is left being attended to by Denning and a stagehand. Peggy slumps to her right, and both Denning and the stage hand move in to help her. However, in the next immediate cut, there is now only Peggy and Denning. Thought it's a closeup of those two, the stagehand's arm and hand still should have been in the frame to Peggy's left.
The word "Premiere" on the marquee of the theatre at the end is spelled without the final "e".
The "42nd Street" finale features full-size cars as well as buildings. In order to present this, the stage would have had to be at least 60 feet deep and over 100 feet wide. This would be impossible in a real theater.
After the chorus line is told to report the following morning for rehearsal, there is a closeup of the sheet music for the song, "It Must Be June". The next shot then picks up the chorus ensemble singing on the 7th music staff, which is a series of quarter notes. However, following the sheet music, the chorus ensemble sings three more additional bars than indicated on it. They sing the lyric "June" four times; however, the music notes on sheet music indicate that it is to be sung only once.
The show's finale performed during the final rehearsal is totally different than the finale on opening night.