Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Lorelai gets home while Rory is on the phone, just as Lorelai jokes about Justin and Britney, filming equipment is visible at the left side of the screen. (00:06:35)
The Lorelais' First Day at Chilton - S1-E2
Continuity mistake: When Lorelai drives Rory to Chilton, the license plate at the front of her Jeep goes from being attached to the center of the bumper, to the side of the bumper, then back to the center of the bumper. Additionally, the Jeep's rearview mirror has vanished when they're parked at Chilton. (00:03:25)
Kill Me Now - S1-E3
Visible crew/equipment: When Lorelai and Emily have a private chat about Rory playing golf with Richard, Lorelai tells her, "You win," and as Emily walks out of the room, the lighting equipment is visible at the left side of the screen. (00:06:00)
Continuity mistake: At Luke's, when Rachel shows Lorelai the photo of the Dragonfly Inn, Rachel says, "It's an old abandoned inn I ran across when I was exploring the other day." So Rachel took the photograph in the last few days, and in the photo the Dragonfly does not have shutters, and does not have a sign hanging over the porch, etc. When Lorelai visits the Dragonfly with Rachel and then with Rory, the shutters and sign have appeared, as well as other changes. (00:04:50 - 00:40:20)
Visible crew/equipment: After Rory asks Lane if Rich still wears the Star Trek shirt, when it cuts to Sookie in the kitchen, we can see two T-marks taped to the floor behind her. (00:08:40)
Visible crew/equipment: When Lorelai and Rory are in the kitchen talking about the to-do list, the camera is visible in the reflection on the microwave. You can see the cameraman's hand rotating the control to move the camera as Lorelai sits down. (00:07:20)
Visible crew/equipment: When Taylor is complaining to Luke, Rory and Lorelai about faded paint, a bright green mic dips above Luke's head. (00:04:35)
Visible crew/equipment: A mic drops into shot just as Jackson accepts Sookie asking him on a date. (00:38:45)
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.