Dear Emily and Richard - S3-E13
Factual error: When Lorelai arrives at the hospital, Rory says she is xeroxing a report that she needs to fax for Sherry because Sherry didn't make enough copies. No matter how many people the report needed to be faxed to, only one original copy would be needed.
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.