The names of the characters who ride the school bus with Danny Gopnik are the names of children that the Coen brothers grew up with.
Most of the doorposts throughout the movie (including the Gopniks' and Mrs. Samsky's) have a small box attached to them. This is a mezuzah, a case containing passages from the Torah (Deuteronomy 6:4-9 and 11:13-21), which Jews traditionally affix to the door frames of their houses as a constant reminder of God's presence. A mezuzah also functions as a sign that a Jewish person occupies the house or works in the building onto which it is affixed, so in this movie, the frequent sight of mezuzahs on doorframes is one of many indications that most of the characters are Jewish.
The song heard on the record played repeatedly in the Gopniks' house is Dem Milners Trern ("The Miller's Tears") by Sidor Belarsky, a Yiddish folk song of a sad miller's fears of growing old and alone, echoing the film's theme.
Tyson Bidner, the film's location manager, was cast as the magbiah at Danny's bar mitzvah because he had been one in real life. He said the Torah scroll was very heavy and difficult to lift above his head.
The cast contains very few Coen regulars, and most of the actors in the film are relative unknowns.