Continuity mistake: There is a scene where Al Pacino is getting dressed for a dinner while talking to one of his aids. He addresses the aide and is seen in a dressing gown with his hair all tousled and untidy. He turns away from the camera, looks in the mirror, and turns back to camera. Miraculously his hair is now tidy as can be, with not a hair out of place!
Continuity mistake: There is a scene in the film when all of the characters are watching a production of Rodgers and Hammerstein's Carousel. Al Pacino and Danny Aiello have a word outside during this. We hear through the doors that the song being sung is "If I Loved You." This song is sung at the very beginning of the production, yet people begin to file out for intermission directly thereafter. They got to the middle of the production pretty quickly.
Other mistake: The Protestant church where the boy's funeral is held has a huge painting of the assumption of Mary to heaven. This is a Roman Catholic doctrine and no Protestant church would have such an image. Even if the congregation bought their building second hand, surely the painting would have been covered up or removed.
Character mistake: At the funeral the Greek mayor makes the sign of the cross in the Roman Catholic way, not the Orthodox way. His hand should have gone from the right to left side of the body.
Factual error: Carousel was not playing on Broadway in 1996, when the movie is set. We see an outside shot of the Carousel marquee on Broadway with the mayor inside watching a full scale production. A U.S. National tour with a scaled-down production began in February 1996 in Houston and closed in May 1997 in Providence, Rhode Island.
Revealing mistake: When Kevin shows the Mayor the Times editorial about the judge he quotes a phrase from the article about whether the man would be a judge if not a former law partner of the mayor. Unlike many newspaper articles shown in films where if you read the article text it is actually jibberish, here it is a legitimate article criticizing the way judges are elected, but some parts are repeated, and it states nothing about the judge being a former law partner of the mayor.