Jane

EMILY: This isn’t funny. I hardly get to see the girl and we only get to talk at dinner once a week and then it’s all about school and Jane.
LORELAI: Lane, Mom.

The fact that Emily mixes up Lane’s name and calls her Jane is a probable allusion to the MTV cartoon Daria (1997-2002), in which protagonist Daria Morgendorffer’s best friend is Jane Lane (I believe this to be source of Lane Kim’s rather unlikely first name).

Jane Lane is not Asian-American like Lane Kim, but her voice actress is Malaysian-born, and the character is drawn with some slight Asian characteristics, so that casual viewers sometimes assume she has Asian heritage. Besides both having black hair and being the less academic sidekick to an intellectual bestie, Jane Lane was a gifted artist, as a parallel to Lane Kim’s musical talent.

(By the way, if Emily only hears about Rory’s doings at Friday Night Dinner, whatever happened to that weekly phone call where she could catch up on Lorelai and Rory’s lives?)

Apple

Lorelai eats an apple while she waits for the pizza to arrive. Much later in the series it is established that Lorelai doesn’t like apples, and only craved them when she was pregnant with Rory. Despite this supposed dislike of fruit, there is always a bowl of fresh fruit on the Gilmores’ kitchen table, including apples. Maybe it’s for Rory.

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.

“Impossible to get away”

EMILY: Regardless the funeral’s on Thursday. I thought we’d all go together.
LORELAI: Ooh, whoa. Two problems. Impossible to get away from the inn Thursday.

We learned in the Pilot that Lorelai attends business class on Thursdays, so she can certainly get away from the inn on that day. Perhaps she means that because of her class, she has to remain at the inn at other hours to make up for it, and that would clash with the funeral. How she knows it would clash when Emily hasn’t told her the time yet is a mystery. Another mystery is why she doesn’t mention her business class as another reason she is booked up on Thursdays.

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.