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.