Much of the movie was filmed out of sequence. In particular when Tony sings "Maria" towards the beginning, it is actually several shots of him walking through the city that were filmed over the course of the four-month shooting schedule. The final note of the song - when Tony sings the word 'Maria' in the alleyway as the camera slowly pulls up and away from him - was the last shot filmed (from the documentary "West Side Memories", 2009).
Richard Beymer and Natalie Wood barely talked to each other in real life. They would say "Good Morning" to each other as if they'd just met, and then start making out when someone said "action." Whenever they finished a scene, Wood would go straight back to her trailer. She wasn't this cold toward many of the other actors in the film. Her ability to cover this up shows her great acting skills. This fact is also mentioned in the West Side Story Special Edition DVD.
Rita Mareno was unable to hit the low notes in the song "A Boy Like That"; the entire song had to be dubbed. Natalie Wood was not told that all of her songs were going to be dubbed until after filming was completed; she went through the production thinking it would be her voice used in the songs when the film was released. Dubbing the songs after filming was completed posed an unusual problem. Normally when a song is dubbed, they play it during filming so that the actors can mouth the words so that they match the lyrics. The songs in West Side Story were dubbed after filming was completed, so it was the singers who were brought in that had to match their lyrics to the actors mouthing the words (from the documentary "West Side Memories", 2009).
In the original stage version Tony and Maria sing "One Hand, One Heart" on the fire escape on the night of the dance. This song was considered too solemn in that scene when the movie was made, so they lifted a tune from "Quintet" and did some lyrics adjustments. The result was "Tonight", which is still the song sung in that particular scene in most stage productions.