When Lorelai takes Luke's truck (1971 Chevrolet Camper Special) to Yale, she struggles to drive a standard shift. In all subsequent scenes, the truck is an automatic transmission.
After Caesar hands Rory the bag of food at Luke's Diner, Rory's position changes from next to the stool to behind the stool between shots.
When Lorelai brings Luke back his truck after the sleepover at Yale, he asked her if she kept it in "park". Much of this episode was about Lorelai learning to drive a manual transmission. There is no "park" on a manual transmission. In addition, when he is showing her a diagram for the stick shift positions, he refers to "reverse" and "drive" -- also not on manual transmission.
Frequent mention is made about Lorelei's lack of knowledge about and ability to drive Luke's truck with a manual (straight drive) transmission. When Lorelei returns Luke's truck he asks her if she left the truck in "park". Manual transmissions do not have a "park" position.
Rory gets annoyed that her ID says "Ronny Gilmore", Lorelei tries to point out that Ronny is a nickname for Veronica. However any school ID would say "Lorelei Gilmore" not "Rory Gilmore".
When Tana nervously tells Paris what the purpose of surnames is, Paris asks what'Tana' means. That is her given name, not her surname, Schrek, which in German can mean 'to jump, or to frighten'