Factual error: Suspended traffic lights didn't exist in fifties NYC.
Factual error: Near the end in Doc's store there are Marvel superhero comics on the rack. The earliest Marvel Comics (Fantastic Four) appeared in 1962. This is supposed to be mid 50's.
Suggested correction: I didn't see any Fantastic Four comics in the scene. It was hard for me to see any titles, but Marvel Comics came out way before 1962. In fact, the first Marvel Comics superhero was Human Torch which debuted in 1939 (Marvel Comics #1). Maybe that's what you saw and were confused. It should be noted that the original Human Torch is not Johnny Storm and wasn't part of the Fantastic Four. If there was a shot of a comic from the 60's, perhaps a scene shot is needed with the name of the title.
Factual error: At the beginning of Quintet, a modern Manhattan skyline is visible in the distance not a late 1950s skyline. Also, the view is consistent with the Paterson, NJ filming location, not the Upper West Side.
Visible crew/equipment: In the officer Krupke song, set lights are visible on the stairs to the audience left and right.
Continuity mistake: When Riff tosses cans at Tony, Tony's right arm is raised. A shot later it's lowered.
Continuity mistake: When Tony lies dead, his head is facing right or left between shots, no continuity whatsoever despite Maria not touching him.
Continuity mistake: When Tony is below Maria's fire escape, there's a shot of her back with her fingers grabbing the platform. Shot changes to Tony's POV where she moves her hand and changes her grip. Then shot goes back to the previous angle of her still with the same grip.
Deliberate mistake: When the gangs meet in the toilets to set a date for the brawl, the mirror on the left is the only one opaque, most surely to avoid reflections of the filming crew.
Audio problem: When the Mambo song starts playing, the bongos player is way out of sync in every single shot.