Other mistake: Rory asks Emily for baby pictures of Lorelai, but Emily says Lorelai burned them all because she had such a big head when she was little. But in "Love and War and Snow" earlier in the season, Emily, Richard and Rory looked at a baby picture of Lorelai in a bunch of petticoats the night Rory stayed over with her grandparents during a snowstorm.
Other mistake: After Lane goes home, when Rory watches her mom talking to Max note the short window over the kitchen sink behind Rory (not the tall window on the same wall). In the next shot, from outside that short window, we see Rory pull the photo strip out of her pocket then proceed to walk to that window and stand directly in front of it. The problem is there should be a sink and cabinets under that window blocking Rory from standing beside the window. (00:43:05)
Other mistake: When Rory and Lane get caught at the movies, Lorelai said she will not lie to Mrs. Kim because she has to respect that Mrs. Kim doesn't want Lane to do something. In reality, Lane is allowed to do things Mrs. Kim would not approve of all the time i.e. Listening to ungodly music, eating pizza, wearing different clothes.