Dear Emily and Richard - S3-E13
Factual error: When Lorelai arrives at the hospital, Rory says she is xeroxing a report that she needs to fax for Sherry because Sherry didn't make enough copies. No matter how many people the report needed to be faxed to, only one original copy would be needed.
Visible crew/equipment: While Dave, Brian, and Zack are in the car, when Mrs. Kim is speaking to Dave the reflection of the boom pole is visible in the window behind Mrs. Kim, then after she leaves when the car starts moving, the reflection of the reflector screen is also visible in Brian's window. (00:31:15)
Visible crew/equipment: When Lorelai returns from her trip she tells Rory that she needs food, and as they walk away from the car, we can see the reflections of the camera operator, camera, and boom mic moving on the surface of the car. (00:38:30)
Continuity mistake: In the scene where Luke and Jess are on the lake discussing in the end, when the camera is on Luke they are in the sun and when it is on Jess they are in the shadow.
Visible crew/equipment: After dinner with Emily, when it cuts to Lorelai and Rory rushing into their house, a c-stand is visible at the right side of the screen at the start of the shot, and a standing spotlight lamp is reflected in the wall mirror. Then as Lorelai walks back down the stairs the camera is visible at the left side of the screen, and when Lorelai exits, the spotlight lamp's reflection is visible again. (00:06:25)
Visible crew/equipment: When Rory (holding the muffins) and Lane are walking on the porch heading to the garage, the reflections of crew, equipment, and the camera operator are visible on the windows. (00:11:05)
Character mistake: In this episode, Rory tells Lorelai that she was cleaning her computer's hard drive because it was full of unopened downloaded files which were consuming her CPU speed. This is wrong, the situation which she's explaining would not use up any extra CPU speed - she may be trying to say her hard drive was extremely fragmented which MIGHT consume some CPU speed (but a tiny amount).
The Big One - S3-E16
Visible crew/equipment: At Chilton, after the teacher returns the graded papers to the students, when she walks to the front of the class her T-mark is visible on the floor. (00:04:55)
The Big One - S3-E16
Visible crew/equipment: When Lorelai and Rory are at Richard's while Emily is away visiting her friends, Richard steps out to answer a call. When Richard returns we can see a blue T-mark taped to the floor behind Rory's side of the sofa. This T-mark is visible again when Richard asks about Rory's speech, because he'd like to be there. (00:20:00)
The Big One - S3-E16
Continuity mistake: When Lorelai sits down on the porch swing at Suki's house to talk, they are both sitting right next to each other, sharing the same blanket. During their conversation, when the shots face each of them individually, you can see there is an empty space beside them on the swing, with both sides of the swing's chains visible. (00:20:50)
The Big One - S3-E16
Continuity mistake: In 1.06 - "Rory's Birthday Parties" Paris says "Ten generations of Gellers have gone to Harvard". In this episode Paris says "Five generations of Gellers have gotten into Harvard"
The Big One - S3-E16
Other mistake: Headmaster Charleston called Rory to discuss the speech contest. His secretary conferenced in Paris. When Headmaster Charleston hung up, the connection between Rory and Paris should have been severed. They were both connected to him, not to each other.
A Tale of Poes and Fire - S3-E17
Visible crew/equipment: When Lorelai has the house-guests due to the inn's fire, Fred Jr. is sitting on the couch and calls her ma'am, then as Lorelai tells the boy to stop because it makes her feel old, the boom mic dips into view at the top of the screen. (00:27:30)
Visible crew/equipment: When Richard walks into the dining room with the treat for the masses and serves Rory this special dish, we can see the boom mic bobbing about in the reflection on the window, at the left side of the screen. (00:00:15)
Visible crew/equipment: While Lorelai and Rory are making a list of everything Luke needs to fix, after Lorelai mentions Dick Van Dyke, the reflections of the camera and a crew member are visible on the left glass door of the corner book cabinet. (00:07:55)
Visible crew/equipment: After Lorelai gets off the phone with Richard, when it cuts to the bakery we can see the reflection of the camera as it moves past the chrome display case. (00:11:50)
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 is visible between the door and frame, slowing the moving door. (00:14:30)
Say Goodnight, Gracie - S3-E20
Visible crew/equipment: After Lane apologizes to Mrs. Kim in the kitchen, when Lane walks to the stairs as the doorbell rings, the reflection of the boom operator holding the boom pole is visible on the glass. (00:29:45)
Say Goodnight, Gracie - S3-E20
Visible crew/equipment: When Luke gets home Jess confronts him about seeing his father, then just as Jess walks behind Luke the two T-marks are visible on the floor. (00:38:15)
Revealing mistake: While Rory and Lorelai are in the kitchen, in a few closeups of Rory we see the refrigerator and counter area with the microwave, etc. behind Rory, but when Lorelai is at the back door about to join Luke, part of the set beside the refrigerator is gone. (00:04:15)
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.