Visible crew/equipment: While Liz and TJ are arguing in Luke's bathroom, when Luke puts the lid on the plastic container with the cheesecake for Lorelai to take home, we can see the shadow of the bouncing boom mic on the cabinet over the stove. (00:36:25)
Continuity mistake: Lorelai and Luke are having a romantic dinner in his apartment. She puts candles in the sticks at an angle, but when they return to the table the candles are straight in their holders. (00:18:00)
Visible crew/equipment: When Rory comes out during the party to meet Dean, he says, "I don't belong here, not anymore, do I?" then as he says, "You look good," a boom mic drops over his head. (00:39:20)
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.