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)
Continuity mistake: At the start, during dinner things on the sideboard move between wideshots and closeups of Rory. Fun to note: when Emily gets up and follows Richard to his seat, as Emily shouts to Siri that Mr. Gilmore is hungry, the camera pans a bit to the left and a water bottle (it's gone in Rory's closeups) has been placed on the sideboard, beside the sterling bud vase, which would cause Emily to have a fit. Obviously one of the actors or the crew left it there.
Star-Crossed Lovers and Other Strangers - S1-E16
Visible crew/equipment: While Lorelai helps her daughter get ready Rory holds up the two sweaters on hangers, and in the shot facing Lorelai as she tells Rory not to clash with the decor, lighting equipment is visible at the right side of the screen. (00:17:50)
Double Date - S1-E12
Visible crew/equipment: While Lane is trying to chat with Todd during the Double Date, when she asks if he likes Fugazi he tells her it's his sister's T-shirt, and just as Lane answers, "Oh," the boom mic dips a bit into view over Lane, at the top of the screen. (00:23:10)
Visible crew/equipment: While Lorelai is cleaning out the fridge, when she picks up the book and asks Rory to give the book back to Max, lighting equipment is visible at the right side of the screen.
Forgiveness and Stuff - S1-E10
Visible crew/equipment: When Lorelai and Dean are talking through Rory's open window, Lorelai tells Dean that they have a nice front door he might want to use, and when Dean walks away the moving boom pole is visible through the top of the glass window, in front of the lattice. (00:13:35)
Other mistake: After Lane goes home, when Rory watches her mom talking to Max note the short window over the kitchen sink behind Rory (not the tall window on the same wall). In the next shot, from outside that short window, we see Rory pull the photo strip out of her pocket then proceed to walk to that window and stand directly in front of it. The problem is there should be a sink and cabinets under that window blocking Rory from standing beside the window. (00:43:05)
Continuity mistake: When Rory comes home from her grandparents and talks to Lorelai about Max sleeping on the couch, into the kitchen and the red-white step stool chair is beside Rory's bedroom door, but when she and Lorelai walk into the kitchen it's gone, then it reappears after Lane leaves. (00:39:45)
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: In the last shot, when Rory starts telling Lorelai all about the market kiss with Dean, some lighting equipment becomes visible at the right side of the screen, as the camera pulls back. (00:43:20)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Emily raves about Sookie's hors d'oeuvres, the shadow of the boom mic is bobbing around at the top of the screen. (00:35:10)
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)
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)
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)
Visible crew/equipment: At the Kim house, when Lane and Rory reach the kitchen doorway, just as Mrs. Kim tells Lane that she has "muffins with no dairy, no sugar, no wheat," the boom pole dips into view at the top right corner of the screen. (00:11:35)
I'm a Kayak, Hear Me Roar - S7-E15
Continuity mistake: When Lorelai picks up Rory and they head off on a drive there is no rearview mirror on the Jeep's windshield, but when they run out of gas and start their walk, a rearview mirror suddenly appears.
Visible crew/equipment: When April shows up at the diner, we can see the reflection of the moving boom pole and mic at the top of the window, behind Luke. (00:14:00)
Introducing Lorelai Planetarium - S7-E8
Continuity mistake: When April and Luke are discussing Sabrina's party, the salt shaker and pepper mill switch places on the table, before April moves them to represent boys and girls. (00:09:40)
Ballrooms and Biscotti - S4-E1
Visible crew/equipment: A mic drops into shot while Lorelai and Luke talk about luggage and the cruise. (00:34:30)
Continuity mistake: Rory is wearing black gloves when she is packing up her car and finds her community service vest, but in the shot facing Lorelai as Rory hands her the vest the glove is gone, then it reappears. (00:04:45)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.