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)
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"
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.
Those Are Strings, Pinocchio - S3-E22
Continuity mistake: During the graduation Lorelai borrows Richard's pen and writes "we got the inn" on the graduation program, and when she holds the program up to show Rory note the position of the blue logo printed on the bottom page. First the logo is near the center crease, but then it's at the outer edge of the page. (00:35:20)
They Shoot Gilmores, Don't They? - S3-E7
Continuity mistake: When Luke fixes Lorelai's shoe, he squeezes glue onto the broken heel and places the glue bottle down on the seat to his left, then he holds the heel to the shoe with both hands, but in the next shot that glue bottle is suddenly back in Luke's hand while he's still holding the heel to the shoe. (00:34:20)
One's Got Class and the Other One Dyes - S3-E4
Continuity mistake: When Lane and the band are arguing in the music shop and Dave ushers Lane to go outside to talk, she picks up her jacket on the way out the door. When she gets outside, though, she has no jacket. (00:09:00)
Continuity mistake: Rory's snow-cone changes color from deep red to light pink between shots.
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)
Take the Deviled Eggs... - S3-E6
Continuity mistake: As Lorelai sits in the car talking to Sherry about attending the baby shower, her seatbelt keeps changing from on or off during the entire scene.
Continuity mistake: When Sookie is reunited with Joe from the Deerhill Lodge, Lorelai pours herself a cup of coffee, then after Joe and Sookie have hugged, in the shots facing Sookie and Joe we see Lorelai's hand holding the cup, but in the shots facing Lorelai and Alex, Lorelai's hands are empty. (00:15:25)
Those Lazy-Hazy-Crazy Days - S3-E1
Continuity mistake: After Luke and "Mimi" talk at the diner Lorelai comes home, and while she and Rory sit on the couch note the open window behind them, with a clown pillow in front of it and the porch chair on the other side, but when Lorelai asks for her purse because she's hungry it cuts to the exterior shot, and nothing is blocking the view through that window. (00:41:00 - 00:43:00)
Continuity mistake: When Lorelai tells Rory she doesn't have to go into the Dean of Admissions' office, Emily is standing right next to her but when Lorelai turns to step away from Rory, Emily is many steps back.
They Shoot Gilmores, Don't They? - S3-E7
Continuity mistake: During the dance marathon while Luke is fixing Lorelai's shoe, Taylor can be seen on the podium in the background changing from standing to sleeping over and over.
Take the Deviled Eggs... - S3-E6
Continuity mistake: During the baby shower while Lorelai and Sherry are talking alone at the food table, all the contents on Sherry's plate keep changing.
Those Lazy-Hazy-Crazy Days - S3-E1
Continuity mistake: In the first shot you can see Rory's laptop open in the background, but when she walks over to her desk and sits down, it's closed. (00:02:15 - 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.