At the beginning of the movie, Luke looks over and sees Dean putting an arm around Rory. However, you can see in the shot before that his arm is already around Rory.
While watching 'Pippi Longstocking' at the Black, White, & Read movie theater, Lorelai asks Dean and Rory to refill the popcorn. They agree and take the popcorn tub and two cups for refills. They return a few minutes later with a full popcorn tub and four refilled drinks, handing two to Luke and Lorelai. Luke and Lorelai did not have drinks to refill.
Emily tells Lorelai and Rory that the panic room can stop a 9mm shell. 9mm handguns do not fire shells. They fire bullets. The only shell related to a 9mm handgun is the bullet's shell casing that ejects from the ejection port after the bullet is fired. But the actual projectile is a bullet.