Like Mother, Like Daughter - S2-E7
Continuity mistake: When Mr. Charleston is looking at Lorelei's parent file, he closes it and starts talking and in the next shot he is seen closing it again.
Rory's Birthday Parties - S1-E6
Continuity mistake: Rory's piece of birthday coffee cake changes sizes throughout the whole scene.
Star-Crossed Lovers and Other Strangers - S1-E16
Visible crew/equipment: While Patty and Taylor argue about the fire and Stars Hollow, there's a mic dip over Lorelai's head right before Luke says "she's bi-polar. And again when Patty says "she is?" (00:13:25)
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.