While the family is having breakfast at the start, Tommy is about to bring a spoonful of cereal to his mouth. However, in the shot right afterward, he dips his spoon into the bowl again.
When Phil is taking Tommy to meet his (Phil's) mother at Saks Fifth Avenue, they stop in front of the statue of Atlas outside Rockefeller Center. In the shot of the two of them talking, with Fifth Avenue in the background, Saks is directly behind them, diagonally across the street on the right, with St. Patrick's Cathedral on the left. However, when Phil looks at his watch and tells Tommy they'd better leave to meet grandma, the two hurry off back north along Fifth Avenue - in the completely opposite direction of the plainly visible Saks.
Early on, when Phil reminisces about his Jewish friend, Dave, he looks into the mirror and assesses his own features as being consistent with those of the Jews. This reveals his own experiences of having been influenced by the false stereotype of there being a "Jewish look". This is antithetical to his attacking anti-Semitic thoughts and actions in others, throughout the film. This, however, should not be considered a "GOOF" as many people are guilty of hypocrisy.
When Phil gets off the train at the Darien station, it actually shows a New York-bound train rather than one from New York. It makes sense visually, because a train from New York wouldn't have had the station building in the shot.