New and Improved Lorelai - S6-E1
Continuity mistake: When Lorelai and Luke are in bed talking about having kids, the first time Luke lies down he is on a blue striped pillow, but the second time it is a light brown pillow.
Continuity mistake: Rory and Lorelai are talking on cell phones and Rory has her hands full with her pencil and her cell phone and every time they cut back to her her hair has been moved around. It goes from being behind her shoulder to in front of her shoulder, then completely behind her neck without her touching it.
Friday Night's Alright for Fighting - S6-E13
Continuity mistake: When Richard hands Rory her martini, she puts it on the table in front of her. In the next shot she puts it down once more.
Continuity mistake: When Loralie is having lunch with Paris, as Paris is leaving at about in Lorelai is wearing tennis shoes. As she walks into the kitchen she has heels on. (00:09:00 - 00:10:00)
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)
The Prodigal Daughter Returns - S6-E9
Continuity mistake: April is in the diner taking a hair sample from Luke and takes his photo. She puts the camera in her pocket and in the next shot she has the camera in her hand again.
Just Like Gwen and Gavin - S6-E12
Continuity mistake: When Lane spins the Doggy Swami wheel, the number 5 is at the top, and Lorelai removes the piece of paper under it. When it changes to the close up shot, the wheel now has the number 20 at the top with the piece of paper under it drawn. (00:40:15)
Continuity mistake: When Lorelai and Luke are talking in bed she is wearing a robe. It goes from on to off her shoulder with each shot.
Welcome to the Dollhouse - S6-E6
Continuity mistake: In this episode, the town voted to change the street names to old timey names. In future episodes, the other names were used. "Peach" was referred to at least twice.
Continuity mistake: When Lorelai enters the kitchen and sees Rory cooking the juicer is visible, but in the next shot you see Rory go to the drawer and get it. (00:25:24)
Just Like Gwen and Gavin - S6-E12
Continuity mistake: April tells Lorelei her dad owns the place and she puts the box of rice down, but when April tells Luke that Lorelei said she wasn't a strangler she puts the box down again.
Friday Night's Alright for Fighting - S6-E13
Continuity mistake: Lorelei is eating marshmallows covered in chocolate syrup. The amount of marshmallows on the plate changes as does the chocolate to marshmallow ratio in the bag next to her.
New and Improved Lorelai - S6-E1
Continuity mistake: During Rory's court appearance the door to the courtroom is closed. When Richard jumps up to yell at the attorney the door is suddenly wide open.
New and Improved Lorelai - S6-E1
Continuity mistake: During Rory's court appearance the gavel and water glass on the judge's desk change positions repeatedly.
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.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.