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: 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: When TJ is at the diner telling Luke about Liz's plans, Luke pours TJ a cup of club soda, and in the shots facing TJ the bottle of club soda is on the counter directly in front of Luke, but in the shots facing Luke the bottle is off to the side near the sugar. (00:11:00)
Continuity mistake: After Lorelai and Christopher bring coffee and donuts to Rory and the other newspaper staff, while Rory's talking to her parents she's holding a blue pencil and papers with no clipboard in sight, but when Chris and Lorelai say goodbye Rory's pencil is black and a clipboard has suddenly appeared in her closeup. (00:40:50)
Continuity mistake: While Lorelai is at the diner talking to Luke about Nicole, when she takes a seat at the counter she places her black purse on the stool beside her, but in the following shots that purse repeatedly reappears and disappears from her shoulder, depending on the camera angle. (00:23:25)
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.
Dead Uncles and Vegetables - S2-E17
Continuity mistake: When Lorelai and Luke are sitting at his kitchen table, there is a box behind Lorelai with a shirt that goes from hanging out of the box to being in the box repeatedly.
Sadie, Sadie - S2-E1
Continuity mistake: When Lorelai and Rory get home from the upsetting dinner from Richard attacking Dean, while sitting at the table one shot shows the Twinkies arranged on the plate in front of Rory on the table. In a few other shots, you see a few twinkies missing and not arranged.
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.
Norman Mailer, I'm Pregnant! - S5-E6
Continuity mistake: Sookie is telling Norman about the menu - twice during this conversation the same inn worker walks into the scene behind her with a duster in his hand.
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)
The Prodigal Daughter Returns - S6-E9
Continuity mistake: At the beginning of the episode, Lorelai can't get in the front door because Luke has installed a chain lock. Near the end of the episode, when Rory returns home and Lorelai rushes out the front door, there is no chain lock present on the door.
Presenting Lorelai Gilmore - S2-E6
Continuity mistake: When Christopher comes to the house and they are all outside talking, there is no garage on the side of the house. Only gates. In later episodes there is a garage.
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.
It Should've Been Lorelai - S2-E14
Continuity mistake: While Lorelai and Christopher are talking at the table at Luke's, a blue coffee mug appears only in one shot but not the rest of the scene.
Continuity mistake: When Lorelai puts her book bag on the table there's an economics book showing and in the next shot it is gone.
Nick & Nora/Sid & Nancy - S2-E5
Continuity mistake: When Rory interviews Max, in each shot the pens on his desk in the cup keep rearranging.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.