Continuity mistake: There is no building next to Luke's in the pilot, but in subsequent episodes there is one, which he buys.
Continuity mistake: While Kirk asks Luke if he is really painting the diner, Luke adds napkins and closes the to-go box twice.
Continuity mistake: While Rory is at Doose's, when Dean surprises Rory and kisses her, in the first shot facing Dean his head is leaning to his left, but in the next shot Dean's head is now suddenly leaning to his right. (00:04:30)
Continuity mistake: Luke is at a table talking to Miss Patty while Lorelai stares out the window at Rory and Lane. Except behind Lorelai you can see Luke at the register alone, even though his voice is still heard talking to Miss Patty.
Continuity mistake: Lorelai and Luke are talking in the storage room. The turkey gravy behind Luke keeps rearranging itself.
Continuity mistake: After the opening credits, Lorelai is watching TV in the kitchen. After she picks up the remote control, the camera angle changes and the TV is gone. It then reappears when Lorelai is standing by the stove. (00:02:35)
Rory's Birthday Parties - S1-E6
Continuity mistake: Lorelai is on the phone with Emily talking about shopping. The apple she is eating changes places with each shot.
The Lorelais' First Day at Chilton - S1-E2
Visible crew/equipment: Right before Miss Patty asks Lorelai if that was what she wore at the Chilton, there is a boom mic's pole showing at the top right corner while she is speaking to the dance class. (00:17:10)
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.