Double Date - S1-E12
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.
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.