Continuity mistake: Rory and Lorelai are talking on cell phones and Rory has her hands full with her pencil and her cell phone and every time they cut back to her her hair has been moved around. It goes from being behind her shoulder to in front of her shoulder, then completely behind her neck without her touching it.
Continuity mistake: When Lane spins the Doggy Swami wheel, the number 5 is at the top, and Lorelai removes the piece of paper under it. When it changes to the close up shot, the wheel now has the number 20 at the top with the piece of paper under it drawn.
Continuity mistake: At the beginning of the episode, Lorelai can't get in the front door because Luke has installed a chain lock. Near the end of the episode, when Rory returns home and Lorelai rushes out the front door, there is no chain lock present on the door.