When Lorelai calls Christopher and asks Rory for the gum wrapper and starts writing Chris's number, in the first and second shot she is actually writing on the gum wrapper but in the next she suddenly has a notebook instead of the gum wrapper.
Before Rory is presented, Lorelai is sitting at the table by herself and in a quick shot her necklace disappears. However, after that quick shot the necklace reappears for the rest of the episode.
When Lorelai makes drinks for herself and Christopher, the shot facing Lorelai has Christopher's drink still sitting on the bar. When the shot changes as Lorelai walks around to be next to him, the drink is suddenly in Christopher's hand.
Rory is supposedly wearing the dress that Lorelai would have worn to her own debutante ball. However, the dress she wears looks nothing like either the one we see Lorelai wearing in a picture in episode 1.8 or the one Lorelai wears in a flashback in episode 3.13.
Lorelai complains to Rory that Christopher's new girlfriend, Sherry, is named after a Journey song, when in fact the song she means, "Oh Sherrie", is by Steve Perry solo, after he left Journey.
When Christopher is showing off his sound system he says "it has 2 subs and 2 12's" which would be 4 sub woofers.