Hugh Jackman took etiquette lessons from 19th-century etiquette expert Jane Gibson (who trained actors for such projects as Sense and Sensibility (1995)). He also studied ballroom dancing and trained to ride a horse for the film.
In the movie, Kate's boss tries to impress her with his knowledge about "La Bohème", but Leopold corrects the boss' mistakes about the opera. For instance, Leopold informs Kate that the name of the male lead is Rodolfo, not Andrè, and that the opera is sung in Italian, not French, although it is set in Paris. The point is that Leopold's travel to the future occurs in 1876, while the world premiere performance of "La Bohème" was in Turin on 1 February 1896. Another point is that the Brooklyn Bridge was dedicated in 1883; however, the Manhattan tower was completed in 1875.
The violin piece being performed during Kate and Leopold's rooftop dinner is Jascha Heifetz's transcription of Leopold Godowsky's "Alt-Wien", or "Old Vienna". Godowsky subtitled his work, originally written for solo piano, "Whose yesterdays look backward with a smile through tears".
The trivia items below may give away important plot points.
In the film's original edit, Stuart was Leopold's descendant, which was Stuart's reason for specifically tracking him down. Criticism that this plot line also meant that Kate was Stuart's ancestor led to those scenes being cut. In the "Director's Cut" version, however, this plot line is followed.
In an early version of the screenplay, Leopold is accidentally transported through time in an actual time machine developed by a group of scientists that includes Kate. They have a child (of whom Leopold is unaware) and eventually reunite during the Roaring '20s.