Norah is a Jewish girl attending a Catholic high school. This is explained in the book that Norah wants to attend any school Caroline does, but due to Caroline's obnoxious behavior, she's kicked out of every school she's been to and is only accepted at a Catholic school.
The film originally opened at The Jerkoffs show where Norah first meets Nick. All prior scenes (including Nick leaving a voicemail on Tris' phone, the scenes with Norah, Caroline, and Tris at the Catholic school, etc.) were re-shoots filmed six months after principal production was wrapped.
Nick's cellphone ring tone is "Boys Don't Cry" by The Cure. (The lyrics tell the story of a man who has given up trying to regain the love of a girl that he has lost, and tries to disguise his true emotional state by "laughing, hiding the tears in [his] eyes, 'cause boys don't cry".)
The trailer shows an alternate version of the club scene kiss with Nick and Norah. When Tris comes up to ask them how they met - it is Nick who tells Tris that they have the same dentist. In the actual movie, Norah is the one that tells this to Tris.