Continuity mistake: When Lorelai and Luke are in Luke's Diner to choose the color for the walls, Luke turns around the 'closed'-sign on the door. In this shot you can see that the venetian blind at the door is quite messed-up; partly closed, partly opened. In the following shot, where all the people are standing outside Luke's Diner looking trough the windows, the venetian blind is orderly and completely opened.
Continuity mistake: In the first scene when Dean brings pizza and they are discussing about Donna Reed: In one shot Lorelai is opening the pizza box and she and Rory take a piece and start eating while they are talking. In the following shot, the piece of pizza in Lorelai's hand is gone and Rory takes a piece from the box - you can see that the pizza is complete again.