The flag of Greece being displayed on the hot dog cart when the boys try to steal it was only adopted by Greece in 1978. At the time of the movie, the flag of Greece was made of a single white cross on blue background.
In the scenes where the adult Shakes and Mike meet in Queens, a train of "Redbird" subway cars is shown passing above them on the "7" line. In 1981, these cars were not yet painted red; they were still painted in their original "World's Fair" colors (turquoise and white) or else were painted all-white.
When the boys are being driven to the detention center, the road is shown painted with double yellow road stripes and yellow 'dashed' center stripes. Dashed center markings were still white until the early 1970s. While many roads still used white solid center markings, double yellow lines had been introduced in the 1950s so they 'may' have been on that road in the mid 1960s.
The R33/R36 cars on the IRT #7 line seen approaching 45 Road station in Long Island City, Queens were not painted red until 1985/1988. Most were in their original turquoise colors in 1981. The MTA "M" logos at the end of each car were not installed on these cars until the late 1980s (1986-88).
In the scene where the boys are lying on the roof right before they steal the hot dog cart, the One Penn Plaza skyscraper in Midtown Manhattan is seen behind Michael. This building was not built until 1972, five years after the scene takes place.
The priest says that it took Michelangelo nine years to paint the Sistine Chapel ceiling. It took 4 years to paint the ceiling. (It took an additional four years or so to paint 'The Last Judgement' on the wall behind the altar.) It took nine years to complete the recent restoration and cleaning of the Michelangelo frescoes in the chapel. The stuff about Michelangelo's father and the loan sharks is obvious embellishment for the kids' sake, but the amount of time it took to paint the ceiling is simply wrong.
During the lunchroom scene at the Home for Boys, Nokes breaks up the fight, and the boys stand in front of him waiting for orders. During this scene, Michael's hand repeatedly jumps from his nose to his hip.
During the trial, the outside scenes are shot at the Manhattan Municipal Building which house city offices, not the courts. The courthouses (federal and state) and the district attorneys office are located a few block north of the municipal building at Foley Square.
Shakes mentioned he will meet Mike at 45 Street in Queens. He gets off the IRT subway at this stop, which is actually 45 Road in Long Island City. The real 45 Street is several miles further east in the Astoria/Sunnyside section of Queens.
Defense Attorney Danny Snyder (Dustin Hoffman) should have moved for a "motion for judgment of acquittal," after the state/prosecution rested their case. No lawyer would fail to make this motion because if it is granted the defense does not have to put on a case since the State failed to meet it's burden of proof during their case in chief. Federal Rules of Criminal Procedure Rule 29 (a) states "after the government closes its evidence or after the close of all the evidence, the court on the defendant's motion must enter a judgment of acquittal of any offense for which the evidence is insufficient to sustain a conviction." New York follows this Federal Rule as discussed in U.S. v. Irving, 682 F.Supp.2d 243 E.D.N.Y.(2010).