While they are waiting for Gypsy to look at the car, Richard asks Dean "how tall are you?". Both actors are quite tall, Edward Herrmann is 6' 5" (1.96 m) and Jared Padalecki is 6' 4" (1.94 m).
First appearance of Gypsy.
The movie that the two boys are looking at and Rory complains about at the beginning of the episode is Showgirls (1995).
Richard says that Lorelai had never invited him to her home before. When he and Emily visited them in Rory's Birthday Parties (2000) it was at Rory's invitation.
Several of the movie and game posters displayed at the video store are ironically very mature titles that certainly would have been cordoned off behind the curtain including Grand Theft Auto, Blow, and Valentine.