At the beginning of the fantasy sequence Gene Kelly falls into a tunnel. When he gets up there is considerable dirt on his white trousers. A few seconds later, when he leaves the tunnel, his trousers are clean again.
When Joe is dancing in the Olvera street sequence he grabs two candles, blows out the flames, then uses the candles as drumsticks hitting some glass balls and other items. The sound given off is of a hard object striking the balls showing that the "candles" are wooden fakes since a wax candle would make a different sound.
Susan Abbott: [sings]
Jealousy, you constantly torture me / I sometimes wonder that this spell I'm under / Can only be a melody for I know no one but me has won your heart.