Hugh Jackman took etiquette lessons from 19-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.
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 lead 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.