Character mistake: This mistake happens in the town meeting scene. They are talking about the two business owners that dated, then moved when it ended badly. It hurt the town's economy. First it was said that Faye sold flowers and the guy sold candy. Then they said that Faye sold candy.
How Many Kropogs to Cape Cod? - S5-E20
Character mistake: On the first day of Rory's internship, she is told she needs to get an ID, to which she replies she never had an ID before, but she got an ID during her first day at Yale, which she and friends later pretended to lose to get new ones.
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.