Women of Questionable Morals - S5-E11
Other mistake: When Rory goes to see her father after Strobe dies, she brings a paper bag with cookies. Christopher comments "and milk", even though the bag was creased. He couldn't see into the bag because the bag is closed.
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.