Audio problem: When Rory and Jess are talking in the car, there's a mismatch sound when Rory says "whatever" followed by "wherever". (00:19:00)
Sadie, Sadie - S2-E1
Continuity mistake: When Lorelai and Rory get home from the upsetting dinner from Richard attacking Dean, while sitting at the table one shot shows the Twinkies arranged on the plate in front of Rory on the table. In a few other shots, you see a few twinkies missing and not arranged.
Like Mother, Like Daughter - S2-E7
Visible crew/equipment: After the Mrs. Backward baseball cap line Lorelai goes to leave. Luke says "and by the way" and there is a camera part showing in the top left corner. (00:42:15)
Presenting Lorelai Gilmore - S2-E6
Other mistake: Dean leaves the house the night before the debutante ball. He says goodbye and leaves the room but he never leaves the house. He never is seen going into the foyer and the door doesn't close.
Presenting Lorelai Gilmore - S2-E6
Continuity mistake: When Christopher comes to the house and they are all outside talking, there is no garage on the side of the house. Only gates. In later episodes there is a garage.
It Should've Been Lorelai - S2-E14
Continuity mistake: While Lorelai and Christopher are talking at the table at Luke's, a blue coffee mug appears only in one shot but not the rest of the scene.
Continuity mistake: When Lorelai puts her book bag on the table there's an economics book showing and in the next shot it is gone.
Nick & Nora/Sid & Nancy - S2-E5
Continuity mistake: When Rory interviews Max, in each shot the pens on his desk in the cup keep rearranging.
The Bracebridge Dinner - S2-E10
Continuity mistake: When Rory is checking in Lane and Mrs Kim, twice in a row it shows her close her folder and hold it at her side and in the next shot it is still open.
Like Mother, Like Daughter - S2-E7
Continuity mistake: When Mr. Charleston is looking at Lorelei's parent file, he closes it and starts talking and in the next shot he is seen closing it again.
Chosen answer: Lorelai and Christopher get married impulsively in Paris but they get divorced shortly after returning home. I don't know the exact number of days or weeks but they definitely weren't married for more than a couple of months.