Those Are Strings, Pinocchio - S3-E22
Stupidity: Richard, an insurance man drove Rory's Prius graduation gift to Chilton. The car wasn't insured, and presumably wasn't registered. An insurance man who is anal about following procedure drove an unregistered and uninsured vehicle? Richard wouldn't do it. Plus, Richard should have mentioned transferring the title to Rory. Can't insure it until it's in her name.
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.