The movie Luke is watching when Lorelai finds him at the theater is My Man Godfrey (1936)
When Luke and Lorelei are watching the black and white movie in the theatre Lorelei says, "they sure talked fast in these things". Gilmore Girls is known for how fast the characters talk.
Janet's final appearance
Matt Czuchry (Logan) & & Katie Walder (Janet) also worked together on episode 1.1, Pilot (2009), of The Good Wife (2009) as Cary Agos & Jennifer Lewis respectively.