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)
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)
Continuity mistake: Lorelai walks into the kitchen and tells Sookie "she did it" and only has a brown bag in her hand. In the next shot she has a brown bag in one hand and the Chilton letter in the other.
Continuity mistake: Dean takes out his salad box when they sit and watch the Donna Reed show, but he doesn't open it. In the next shot it is open, and in the next shot again, a salad leaf is at his fork, without touching it.
The Lorelais' First Day at Chilton - S1-E2
Continuity mistake: While Rory is at the administration office Miss James gives her the Chilton map, schedule, etc. Then just as Miss James tells Rory that Mr. Winters, the guidance counselor, handles everything except bulimia and pregnancy, Miss James is wearing eyeglasses in the shot facing Rory, but in the previous and following shots she is not. (00:15:50)
Forgiveness and Stuff - S1-E10
Continuity mistake: When Miss Patty finds Rory and Dean asleep, they are asleep face to face. In a subsequent shot they are lying on their sides, Dean behind her.
Continuity mistake: There is no building next to Luke's in the pilot, but in subsequent episodes there is one, which he buys.
Continuity mistake: While Kirk asks Luke if he is really painting the diner, Luke adds napkins and closes the to-go box twice.
Continuity mistake: While Rory is at Doose's, when Dean surprises Rory and kisses her, in the first shot facing Dean his head is leaning to his left, but in the next shot Dean's head is now suddenly leaning to his right. (00:04:30)
Continuity mistake: Luke is at a table talking to Miss Patty while Lorelai stares out the window at Rory and Lane. Except behind Lorelai you can see Luke at the register alone, even though his voice is still heard talking to Miss Patty.
Continuity mistake: Lorelai and Luke are talking in the storage room. The turkey gravy behind Luke keeps rearranging itself.
Continuity mistake: After the opening credits, Lorelai is watching TV in the kitchen. After she picks up the remote control, the camera angle changes and the TV is gone. It then reappears when Lorelai is standing by the stove. (00:02:35)
Rory's Birthday Parties - S1-E6
Continuity mistake: Lorelai is on the phone with Emily talking about shopping. The apple she is eating changes places with each shot.
Rory's Birthday Parties - S1-E6
Continuity mistake: Rory's piece of birthday coffee cake changes sizes throughout the whole scene.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.