When Luke comes over to tell Lorelai about Jess, he's beckoning from outside the back kitchen door. However, as Lorelai goes through the door and the camera angle changes, they're standing in front of the side living room door.
When Paris and Lorelai are selling tickets for the Grad Night Cruise, Paris asks Lorelai to unbutton her top, to encourage the teenage boys to approach them, but Lorelai refuses and tells Paris to 'stop looking at my boobs'. But when the camera angle changes, Lorelai's top button is undone.
When Sasha was talking about Jess' father going to bee him, she said that they hadn't seen each other for 17 years, whereas when Luke goes over to Lorelai's to tell her that Jess has left, he says that Jess is 18 years old. This doesn't pan out because it is repeatedly said that Jimmy left the day that Jess was born.
Lorelai says that she and Rory have dinner at Souplantation, which is a California-based chain restaurant. Though it has expanded outside California there are no locations in the Northeast US and all locations outside Southern California are called Sweet Tomatoes.
The plot regarding Rory's Yale financial aid has a number of problems. First, there is no way the school would know about Lorelai's recent investment windfall, as they would be working from a FAFSA form using the previous year's tax return. Second, schools competing for good students like Rory would likely offer aid beyond income-based federal aid. It's quite rare for anyone to pay sticker price for any university, including Ivies. Third, financial aid offers are typically made at the time of acceptance letters, and so Rory would have had this information long ago and used it to decide which university to attend.
When Luke and Lorelai are talking on the porch, a crew member can be seen reflected in the window.
Sasha mentions the Gatekeeper with a beard on "The Wizard of Oz" to Jess. While the Gatekeeper on the movie does sport a mustache, he has no beard.