Rory's Dance - S1-E9
Factual error: The morning after Dean and Rory fall asleep at Miss Patty's, when Patty wakes them up, she tells them it's five-thirty in the morning. When Rory runs out into the street, there is snow on the ground and the sun is up. In Connecticut, there is no time of year in which there would be both snow on the ground and sunlight at 5:30 a.m. (It's not streetlights either - in other episodes that take place at night in the town square, the streetlights do not light up the entire square - they are some distance apart, and their light is concentrated around the poles).
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.