Rory mentions her and Lorelai's plan to backpack around Europe when she graduates high school and Richard is supportive of the plan and the trip. When it is mentioned later in the series, Richard acts as though he has never heard of this plan, and he and Emily act amused at the plan and appalled that the girls would backpack.
Lorelai is sat at the porch table, and Rory returns with a bottle of oil. After that, the items on the table (water bottles, blue mirror) keep changing places and positions (and the bottle of oil keeps rotating, note the way the labels face).
Lorelai and Rory are sitting at a table, with Rory looking at herself in a mirror, they talk about Rory's hair. Right after this, Rory asks, "Do you want something to drink?" and her mouth doesn't move at all.
Right after Lorelai asks one of her employees at the inn to "send Rory up to room 12 in about 10 minutes", she tells another one of her employees that her father and Rory are out golfing at his country club that day. Unless Rory was in two places at once, it would be impossible for her to go to to room 12 in 10 minutes when she was not even on the property.