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. (00:36:00 - 00:36:45)
Factual error: At the end of the movie Saoirse Ronan enters the US through the US Citizen's lane. After being married for 1 month she would not have yet qualified for citizenship.
Factual error: The boat from Ireland to America has the sun high in the sky (i.e. in the south) but the boat is travelling the wrong way for this to happen. The way it is shot, the sun is in the north - which is an impossibility. (00:11:00 - 00:12:00)