Near the end, when Maria yells "Don't you touch him!", two different voices can be heard at the same time in the first half of the phrase (in fact, this is singer Marni Nixon overdubbing for Natalie Wood).
When Doc says, "What are you doing there?" after stopping the Jets from taunting Anita in the drugstore, his lips actually mouth, "What are you doing now?" which was the line in the original stage script.
The Jets sing "The Jets are gonna have their day tonight. The Jets are gonna have their way tonight". One of the voices sings "way" instead of "day" in the first line, so the result sounds like "dway".
Chino visits Maria on the rooftop, saying that there was no-one home. Maria tells that her parents are at work. Only a few moments afterwards we hear voices: "¡Mamá, Mamá! ¡Bernardo está muerto!" "¿Bernardo? ¿Muerto?", the latter apparently said by the mother.
At the beginning of the movie, behind the first close-up of Riff on the playground, snapping his fingers, you can see a young boy riding his bike behind Riff, the boy wasn't there in the previous shot (from above).
After the war council, Schrank says that he rebuked the Jets the same day. That means that all events before the war council were on that day too. The dance started at 10 PM, and that leaves very little time for America, the balcony scene and the war council.
During the rumble (the big fight between the Jets and the Sharks), Bernardo gets cut in the back by Riff. During the fight, there is no cut on the back of Bernardo. Whilst lying on the ground after he's killed, there is a big cut across his back.