Factual error: The year is 1952. In an exterior scene, Saoirse Ronan is seen on a street in Brooklyn. In the far background, a red "WALK/DON'T WALK" sign is flashing. This type of sign was only introduced across NY in the late 50s.
Continuity mistake: When Eilis has dinner with Tony's family for the first time, everyone is eating spaghetti. When the little brother returns at end of the scene, they are eating meat and vegetables, which you can also see being served on the table as well as each individual plate.