A Messenger, Nothing More - S5-E2
Continuity mistake: Lorelai's hair is once curly, once straightened in every other shot after she leaves her house with Rory up until she meets Luke. (00:31:45)
We Got Us a Pippi Virgin - S5-E5
Continuity mistake: When they are starting Pippi and Luke is asking about her hair, you can see Dean's hand on Rory's shoulder on the side of the shot. Then it pans to them and then Dean is putting his arm around Rory.
Norman Mailer, I'm Pregnant! - S5-E6
Continuity mistake: Sookie is telling Norman about the menu - twice during this conversation the same inn worker walks into the scene behind her with a duster in his hand.
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)
Continuity mistake: When Lorelai and Christopher are at the inn Georgia is with them at the table in her high chair, but in a few shots the high chair is empty despite the fact that Lorelai supposedly turns to talk to Georgia.
But Not as Cute as Pushkin - S5-E10
Continuity mistake: When Paris goes to speed dating Rory tells her it's 11 at night and her hair is up, but during speed dating, her hair is down and its daylight outside.
Continuity mistake: When Rory and Paris sit down to eat cereal in the cafeteria, the table has dirty dishes on it, but when they call over the girls, the table is clear.
Continuity mistake: When Lane delivers lunch from Luke's to Rory in the bookstore, the couple seen outside (man in black jacket and woman in white coat) are seen approaching and picking up a magazine not once but four times. They re-approach and pick up the magazine in each camera shot of Lane. (00:27:45)
A House Is Not a Home - S5-E22
Continuity mistake: When Lorelai is talking to Richard and Emily about Rory, Richard writes down the name of an attorney and closes his memo pad but in the next shot it is open again with his pen poised.
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.