Continuity mistake: At the end of the "Bye, Bye Baby" song the two girls are standing at the railing with two people in between them and the detective. When the shot cuts to their backs the two people in between the detective and the girls have disappeared.
Continuity mistake: In the scene where Marilyn Monroe sings "Diamonds Are A Girl's Best Friend", her hair is styled in a sleek bob. In the dressing room scene directly following the musical number, Marilyn has supposedly just walked off stage, but her hair has transformed from sleek to curly.
Other mistake: During Dorothy's and the detective's date, they are outside while the boat is moving, yet there is no wind blowing around. Since the ship is moving there should be wing blowing past the two.
Factual error: The "Olympic team" sailing on the ship consists of approximately 18 men. The actual 1952 US Olympic team consisted of 286 competitors (245 men and 41 women), plus a large number of coaches, trainers, and so on.