Say Goodbye to Daisy Miller - S5-E1
Visible crew/equipment: Near the start, after Rory tells Lorelai that Dean came over to borrow something, just as Dean opens the door the reflection of a crew member is visible on the door's window. (00:02:50)
Say Goodbye to Daisy Miller - S5-E1
Visible crew/equipment: At the start of the shot as Emily's luggage is placed beside the car and Emily is about to walk out the door, the boom pole is visible at the top left side of the screen and the boom mic is visible at the top center of the screen. (00:38:40)
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)
Visible crew/equipment: When Maisy sends Buddy to the kitchen to bring Luke and Lorelai the food without garlic, in the next shot just as Maisy tells Lorelai, "It's nice to meet you," the tape mark is visible on the floor behind Maisy's feet. (00:17:35)
Character mistake: This mistake happens in the town meeting scene. They are talking about the two business owners that dated, then moved when it ended badly. It hurt the town's economy. First it was said that Faye sold flowers and the guy sold candy. Then they said that Faye sold candy.
Tippecanoe and Taylor, Too - S5-E4
Visible crew/equipment: After Lane and her bandmates listen to the tape with the song Believe It or Not (theme song of The Greatest American Hero), when Zack says, "I'm not wearing smelly wood on my face," the T-mark is visible on the floor at Brian's feet. (00:29:00)
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
Visible crew/equipment: While Lorelai is looking for her keys, when she takes her toasty socks out of the oven and puts them on, the T-mark is visible on the floor beside her. (00:01:20)
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)
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)
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)
Visible crew/equipment: After Emily asks Lorelai to help her with dating etiquette, when Lorelai and Rory leave the house some filming equipment is visible at the top left side of the screen. (00:20:20)
Visible crew/equipment: When Lorelai and Christopher are at the Dragonfly looking at the lunch menu, filming equipment (looks like the second camera) is visible at the left side of the screen, and it's visible again when Lorelai describes Michel and the bathrobe bandits. (00:22:15)
Visible crew/equipment: When Loralie walks out of the kitchen with a bowl of popcorn you can see the camera is slightly covered on the left side of the screen. (00:49:53)
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.
Women of Questionable Morals - S5-E11
Other mistake: When Rory goes to see her father after Strobe dies, she brings a paper bag with cookies. Christopher comments "and milk", even though the bag was creased. He couldn't see into the bag because the bag is closed.
Visible crew/equipment: During the Dragonfly's staff meeting, when Michel stands up and announces, "We have a problem with some honor bar discrepancies," the T-mark is visible on the floor between Michel and Lorelai. (00:06:30)
Other mistake: Lorelei, Rory, and Luke are about to leave for Emily and Richard's wedding. Babette is on the sofa half passed out from the bachelorette party. When she hears Lorelei speak her name her head pops up to say goodbye, and she also comments that Luke looks nice. Luke is wearing a long overcoat. She could not possibly see how he looks, plus she was viewing him from behind.
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.