In 1968, Noodles returns to the train station and opens a briefcase full of money. As he gets set to close the briefcase, we hear the chug-chug of a steam locomotive starting up in the background, then a steam whistle sounds. New York City banned steam locomotives in 1860. In the US, most steam engines were replaced with diesel locomotives by 1958.
In November, 1968, when Noodles visits the locker in the station and pulls out a wad of US Currency, the top bill is signed by W. Michael Blumenthal, President Carter's Secretary of the Treasury from January 23, 1977, to August 4, 1979.
Just before the boys demonstrate the salt trick to the Italians, fluorescent lighting is visible inside the large buildings in the background. Flourescent lights weren't commercially available until the 1940's.
During the Famous scene where the young boys are crossing the street with the Manhattan bridge in the background, the building on the right has a visible window air conditioner, something that was not available until 1932.
During the scene when the young boys set the newspaper stand on fire, they run around the corner and peek through a window in the concrete which has visible spray painted graffiti on the wall, spray paint was not invented until 1949, this scene takes place in the 1920s.
While Dominic looks at himself in the mirror, just after the boys talk about the deadbeat newsstand vendor, a lady can be seen behind him picking up a 50-star U.S. flag. But the flag in 1920 had 48 stars.
Noodles watches a 1967 telecast concerning the investigation revolving around Chairman Bailey (on a decidedly European-looking television set). Twice during the telecast, we see a cameraman with a portable video camera and an assistant with a portable videotape recorder. The very first Electronic News Gathering (ENG) equipment wasn't available in the US until at least 1971.
When young Noodles holds young Peggy in the toilet and she says "You better stop squeezing me, or I'm gonna poop in my pants", the beginning of her line sounds twice, as if two different takes have been overlapped with a cross fade.
In the very first scene, when the woman is shot, her shirt is covered in blood. When she is shot again, even more blood stains her shirt, but when she falls back, her shirt is completely free of blood.
Early, when the guy is being beaten, the thugs shoot the punching bag next to his head to scare him - the shot is fired with a semiautomatic pistol with a silencer. The thug then puts the silencer in the guy's mouth and cocks the hammer of the pistol - since it is a semiautomatic, the hammer should have already been cocked.
When Noodles is visiting Deborah, during the various cuts when she is telling him to take the back door out, the makeup is almost gone. When she is standing by the door the make up is back in places. Also through the conversation the make up disappears and shows up in places.
When Noodles first meets the adult Deborah (1.45:30) his hair is dry and neatly combed but moments later he walks through a door to first meet Frankie Manoldi and his hair is noticeably oily and more tousled.
When Deborah's train leaves for Hollywood, a French railroad car (SNCF) is on a track in the background. Above the French car, a sign can be seen saying "Voie 13", which is French for Track 13, indicating this scene was shot at a French railway station.
When Noodles talks to Deborah in the dressing room after her play, every time she raises her voice it reverberates like she'd be talking in a big hall - which is because the small dressing room is a set, presumably with one wall and the ceiling missing, built on a big sound stage.
The goof item below may give away important plot points.
When we see Max walk toward the garbage truck and supposedly get into the back to be ground up and killed, you can see the actor's feet running alongside the truck (by the rear wheel) as it starts to move.