“I don’t tap any more”

[The girls start dancing. Kirk watches them as Rory walks over to him.]
RORY: How come you’re not up there Kirk?
KIRK: Oh, I don’t tap anymore. Bum knees.

This is the first indication we have of Kirk’s artistic leanings and dance training, later retconned so that he is actually a past student of Miss Patty (even though he had never met her in their first encounter on the show, in Cinnamon’s Wake).

“I don’t have any baby pictures of your mother”

EMILY: I don’t have any baby pictures of your mother.
RORY: How could you not have any baby pictures of Mom?
EMILY: Because when your mother was seven, I came downstairs and found her burning all of her baby pictures.

Emily already showed Rory a baby picture of Lorelai in the family photo album when she was staying at her grandparents’ house in Love and War and Snow, so this is a retcon.

“Finally got off the septic tank system”

RORY: Well, this is a town that likes the celebrating. Last year we had a month long carnival when we finally got off the septic tank system.
DEAN: A month long? You’re kidding.
RORY: No. There were rides and a petting zoo and balloon animals and a freak show.
DEAN: Uh huh. Okay, you almost had me going there for a second.
RORY: Well, we did have a ribbon cutting ceremony.

A septic tank system is one where domestic sewage flows into for basic treatment. The “fecal sludge” (poo) does not break down fast enough, and will periodically need to be taken away in a truck. It’s an onsite sewage facility used in areas not connected to a sewerage system, especially rural areas, such as on farms.

From Rory’s comment we learn that Stars Hollow got off the septic tank system in early-ish 2000 to be connected to the main sewerage system. For some reason, that was retconned in the revival so that the town was still on the septic tank system.

Cinnamon

As Lorelai and Rory leave the house to go to work/school, they meet their neighbours Babette and Morey taking their cat Cinnamon for a walk in a covered wagon. We first heard about Cinnamon in Kill Me Now, when Babette identified Cinnamon as male, by saying “he” was stuck under the porch. Since then, Cinnamon has had a sex change, as Babette says that “she” likes to be taken for walks.

Mr. Medina

When the scene changes to Rory’s English Literature class, the teacher is now Mr. Max Medina (Scott Cohen). However, when Rory first started at Chilton two episodes ago, her English Literature teacher was Mr. Remmy (John Billingsley).

There is no attempt made to explain this away, such as Mr. Remmy suddenly leaving and Mr. Medina taking his place, or Mr. Remmy having filled in temporarily while Mr. Medina is sick (Mr. Medina says they’ve been studying Shakespeare for the past three weeks). It is just retconned as Mr. Medina having always been the English Literature teacher and Mr. Remmy never existing.

You can try to explain it as Mr. Remmy being the English teacher and Mr. Medina taking the English Literature class, except that if you add up all Rory’s subjects that she takes in her first semester, that would give her too many classes to attend. It also doesn’t quite gel with Rory being behind in her reading for Mr. Remmy’s class, and then getting a D in Mr. Medina’s class because she was behind in her reading.

The decision seems to have been made to match Lorelai up with Rory’s teacher, and Mr. Remmy wasn’t going to cut it as a love interest, thus entering Mr. Max Medina. The best-selling novel The Princess Diaries by Meg Cabot had just been released in October 2000, which featured a teenage girl living with her single mother, and the mother began a relationship with the heroine’s Algebra teacher. Either this was an influence on Gilmore Girls, or it’s an example of zeitgeist.

Actor Scott Cohen does have some experience at the front of a school classroom: in his twenties he spent some time as a substitute teacher, teaching music to kindergarten children at an elementary school in Queens, New York. He was offered a permanent position, but had to turn them down so he could concentrate on his acting career. He and Lauren Graham, who plays Lorelai, were already friends before they starred in Gilmore Girls as a couple.