Anything GoesGoofs
Continuity
During the "Ya Gotta Give The People Hoke" number Bing Crosby and Donald O'Connor go into a prop room, pick up a prop, go on stage, do a "bit" and go back to the prop room. About midway through, Bing comes out on stage wearing a Fireman's hat. There is a pile of brownish debris and several piles of white material that were not there a second before, indicating that one or more "bits" had been cut after filming.
Revealing mistakes
During the "You're The Top" number Bing Crosby and Mitzi Gaynor are on the lifeboat deck on one side of a partition while Donald O'Connor and Zizi Jeanmaire are on the other side. All are singing yet, though the deck is open to the sky, no one hears the others. Also, there are no partitions on a lifeboat deck.
Audio/visual unsynchronised
During the dancing for "It's De-lovely" there are more footsteps in the sound track than they are making with their feet.