The Mambo Kings (1992)
The poster is visible in a store near to the police station.
Mentioned in conversation between Ryan, Pippa and Sophie
Jay says he gave thumbs up to the movie
Daphne and her friends say they want to watch this.
Caitlin tells Paul she's watching it.
Lorelai says that Emily has Rory "locked in here with the Mambo Kings."
Honorable mention, clips show