Continuity mistake: When Lorelai and Luke are talking in bed she is wearing a robe. It goes from on to off her shoulder with each shot.
Star-Crossed Lovers and Other Strangers - S1-E16
Visible crew/equipment: When Rory asks Lorelai to call Emily to get her out of Friday night dinner so she can celebrate her and Dean's 3-month anniversary, a boom mic drops into the shot as Lorelai stands to get the phone. (00:07:05)
Red Light on the Wedding Night - S2-E3
Continuity mistake: When Lorelai, Rory and Max are having breakfast at Luke's, their coffee cups change from red to blue in one shot. Also Max's coffee cup goes back and forth from the left side of his paper to the right. (00:14:50)
Star-Crossed Lovers and Other Strangers - S1-E16
Visible crew/equipment: During Friday night dinner, after Emily suggests brandy in the living room Lorelai excuses herself, and when she stands up in the wideshot the boom operator can be seen at the left side of the screen. (00:31:25)
Super Grover
Visible crew/equipment: When Rory gets the photo album from her mother's bedroom and shows her grandparents, just as Emily reminds Richard about getting the baby dress in London, a piece of filming equipment can be seen at the right side of the screen. (00:27:25)
Super Grover 
Visible crew/equipment: After Rory tells Lorelai that she looks happy, when it cuts to Max telling his class about Emily Dickinson's poem, the boom mic can be seen bobbing around at the top of the screen. (00:07:55)
Super Grover Continuity mistake: Kirk introduces himself as "Mick" in the second episode. From episode 3 and throughout the series his name is "Kirk."
Continuity mistake: When Luke knocks on the kitchen door (at the back of the house) and calls Lorelai out to talk on the back porch, Lorelai grabs the doorknob to go out that door, but in the very next shot from outside Lorelai is actually walking out of the side living room door which is at the side of the house while Luke is standing there. Two completely different doors, at different sides of the house, and the back porch is not connected to the side/front porch. (00:06:10)
Visible crew/equipment: At the start of the episode Rory and Lorelai are about to open the garage door. You can see a crew member in the reflection of the glass moving his arms around the camera - you can also slightly see his head for a split second. (00:39:00)
Roshe
Eight O'Clock at the Oasis - S3-E5
Visible crew/equipment: When Emily gives Lorelai and Rory their drinks she mentions the cheese and walks away, then when Lorelai sits on the sofa the green tape marks can be seen on the floor, where Emily had been standing by the bar. (00:40:20)
Super Grover 
Visible crew/equipment: When Lorelai argues with Richard in his study, nothing gets resolved and Richard says that he's tired, then in the last shot of Lorelai a crewmember's fingers can be seen holding equipment at the right side of the screen. (00:25:55)
Super Grover 
Visible crew/equipment: When Luke is waiting for Lorelai to show up and paint, a crew member, camera, and boom mic are reflected in the window next to him. (00:29:45)
jkwebsterContinuity mistake: When Lorelai and Luke are in Luke's Diner to choose the color for the walls, Luke turns around the 'closed'-sign on the door. In this shot the venetian blind at the door is quite messed-up; partly closed, partly opened. In the following shot, where all the people are standing outside Luke's Diner looking through the windows, the venetian blind is orderly and completely opened.
Other mistake: When Rory is dropped off in the morning after spending the night with her grandparents, she walks from the car to the porch where Lorelai is standing, but even though it's snowing there aren't any snowflakes anywhere on Rory. (00:39:10)
Continuity mistake: In the first scene when Dean brings pizza and they are discussing about Donna Reed, in one shot Lorelai is opening the pizza box and she and Rory take a piece and start eating while they are talking. In the following shot, the piece of pizza in Lorelai's hand is gone and Rory takes a piece from the box - you can see that the pizza is complete again.
Haunted Leg - S3-E2
Visible crew/equipment: When the new maid tells Emily the dinner is ready even though it's only 6:30, Emily concedes and they all head to the dining room, and just as Emily says they all can be in bed by 9:00, the boom pole and mic can be seen in the living room behind them, at the top of the screen. (00:33:20)
Super Grover Haunted Leg - S3-E2
Visible crew/equipment: After Emily tells the new maid it would wonderful to remember the difference between the bells, as Emily, Lorelai, and Rory walk away from the front door, the white, red, yellow, and green tape marks can be seen on the floor behind them. (00:32:00)
Super Grover 
Visible crew/equipment: When Jess shows up at Principal Merton's office because he couldn't get prom tickets, as Jess shuts the office door the hand of a crew member can be seen between the door and frame, slowing the moving door. (00:14:30)
Super Grover 
Back in the Saddle Again - S2-E18
Visible crew/equipment: When Emily opens the door for Lorelai and Rory for Friday night dinner, they walk in and sit in the living room, then during their conversation four T-marks can be seen taped to the floor behind Emily. (00:37:40)
Super Grover 
Continuity mistake: While Lorelai and Rory are at Luke's for a very early breakfast, when Miss Patty walks in she's wearing long earrings, but the earrings vanish and then reappear while she's telling Lorelai how badly she feels about Rory and Dean. (00:13:15)
Super Grover 
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.