Continuity mistake: When Sean shows up to meet with Mary Kate and her brother he is carrying pink roses. The entire time he is in the house the roses are now red.
Other mistake: In Gene Kelly's 'Singing in the Rain' sequence, the taps he makes do not match up with the actual movements of his feet - they are much more complicated than the steps he makes. Since one can't tap dance in wet loafers, Kelly had to do the dance in the studio, and the taps were added into the picture. He apparently got a little overzealous.
Other mistake: During the car chase an Indian shoots an arrow that bounces off the car's license plate and comes back and hits the Indian. But a second before the arrow hits the Indian you can see him sitting on his horse with his eyes closed and a look of pain on his face as though the arrow had already hit him.
Continuity mistake: As Lana Turner and Kirk Douglas are toasting with champagne, the cigarette she is holding disappears.
Continuity mistake: In the scene where Bing Crosby is talking to Ethel Barrymore at a picnic day for the girls of he very snobbish school, he makes a big deal out of taking out a cigarette and lighting it, but in the next shot - no cigarette.
Other mistake: Before the trial by combat, when Richard Taylor and George Sanders choose their weapons, they are brought to them on their shields. But this happens to quickly, right after the choices were announced, as if predetermined.
Factual error: Players didn't wear numbers on uniforms at that time.
Factual error: In Danny Kaye's song about "The Emperor's New Clothes" he persistently and repeatedly uses the words "the king is in the altogether." Hans Christian Andersen lived from 1805 to 1875, but the expression "in the altogether", meaning naked, was invented and popularised by George Du Maurier in his novel "Trilby" which was not published until 1894.
Revealing mistake: In the opening scene the Club's dancers are in full-swing, including the tall, lanky gentleman from Lautrec's famous Moulin Rouge poster, the one with the very angular, extended nose and chin. In several closeups it's very plain that the chin is a makeup appliance: the edge of the appliance isn't blended very well with the actor's real skin.