When the boys are lying on the roof right before they steal the hot dog cart, the One Penn Plaza skyscraper in Midtown Manhattan is visible behind Michael. That was built in 1972, five years after the scene takes place.
The R33/R36 cars on the IRT #7 line that approach 45 Road station in Long Island City, Queens were not painted red until 1985 or 1988. Most turquoise colors in 1981. The MTA "M" logos at the end of each car were added in 1986.
The priest says that it took Michelangelo 9 years to paint the Sistine Chapel ceiling. It took 4 years to paint the ceiling, and 4 more to paint 'The Last Judgement' on the wall behind the altar. The recent restoration and cleaning of the Michelangelo frescoes in the chapel took 9 years.
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 at Foley Square, a few block north of the municipal building.
Shakes says he will meet Mike at 45th Street in Queens. He gets off the IRT subway at 45th Road in Long Island City. The real 45th Street is several miles further east, in the Astoria/Sunnyside section of Queens.
Defense Attorney Danny Snyder should have moved for a "motion for judgment of acquittal" after the state/prosecution rested their case. No lawyer would fail to make that motion because if granted, the defense does not have to put on a case because the State failed to meet its 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).
When the boys are being driven to the detention center, the road has 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.
When John Riley tells the bar tender to give the two men drinks at the end of the bar, the camera angle is from about halfway down the bar. A radiator is visible in the dining area in the back, but no tables or people are visible. When John comes back from the men's room and tells Tommy to look in the back room, Sean Nokes is visible from where they sit. He was not visible earlier because he was not in view from the bar until John walked into the room and saw him sitting there at a table by the window. The table was out of sight until Tommy looked in that direction.
At the end of the movie during the reunion, the men reflect back on their boyhood singing group before they entered the youth facility. They mention that one of the members wanted to name the group "The Count and his Cristo's" after the book that he read while in the juvenile facility. The time line doesn't make sense. He wouldn't have proposed the name before they entered the facility because the story didn't mean anything to them then. It wouldn't have made sense for them to talk about naming the group after they were imprisoned.
The goof items below may give away important plot points.
When John and Tommy enter McHale's as adults, an elderly couple are entering the dining room portion along with a waitress. The man removes his hat and heads for a table with his wife. Neither the couple nor the waitress are in the room while John walks in and later when he and Tommy shoot Sean Nokes.
When John and Tommy kill Sean Nokes in the dining room of McHale's, they use semi-automatic hand guns. However, neither gun ejects shell casings, and they did not stop to pick up the brass that would've been ejected.