Visible crew/equipment: While Dean is watching the play rehearsal, when Tristan starts talking about the "first kiss" in the wideshots facing Dean, we can see the boom pole moving at the top right corner of the screen. The boom pole is not part of the student production. (00:33:30)
Continuity mistake: Lorelei's casual date brings his parents into Luke's and even though the windows are covered and you can't see outside, the cash register is at the wrong end of the counter.
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.