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.
Always a Godmother, Never a God - S6-E4
Stupidity: Rory arrives in Star's Hollow for the baptism. She parks presumably near the church. When she gets out of the car, she does not have a purse or car keys in hand. She apparently left the car unlocked and left the keys in it. It's just plain dumb.
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.