At one part, Petrov is standing in front of a full-length mirror talking to Jeffrey. The reflection in the mirror doesn't match the actor's (or stand-in) playing Petrov's movements.
At the end, Linda Keene (Ginger Rogers) plans to crash Petrov's (Fred Astaire) big dance number, so she can personally serve him her divorce papers. Legally, a summons cannot be served by someone who is a party to the action.
The newspaper displaying the incriminating bedroom photos is the fictional "New York Dispatch" in closeups, but the real life New York American in long shots. Little more than a month after this film's release, the American merged with the Evening Journal to become the New York Journal-American (1937-67).
At the launch of the air mail plane from the ship, the plane engine is heard to be idling. The engine would be at full power.