Other mistake: Lorelai is in bed post breakup. Rory returns from running errands for her. She comes upstairs with Frank who is carrying the television. Frank puts down the television and leaves. When Rory leaves, Lorelei turns on the TV. No one plugged it in or hooked up the cable, assuming that cable is installed in her bedroom (which is extremely doubtful). Lorelai would not have been able to flip through channels as she did.
Continuity mistake: When Rory and Paris sit down to eat cereal in the cafeteria, the table has dirty dishes on it, but when they call over the girls, the table is clear.
Continuity mistake: When Lane delivers lunch from Luke's to Rory in the bookstore, the couple seen outside (man in black jacket and woman in white coat) are seen approaching and picking up a magazine not once but four times. They re-approach and pick up the magazine in each camera shot of Lane. (00:27:45)
Visible crew/equipment: When Emily enters the diner and says hello to Luke, two yellow T-marks are taped to the floor, then when she approaches the counter the actor's blue tape mark is visible at Luke's feet, and as Luke walks to the coffeemaker another tape mark becomes visible. (00:40:20)
Visible crew/equipment: At the start, Lorelai brings home the bags of assorted tacos, and when Lorelai stands at the counter pouring coffee, we can see the red T-mark taped to the floor where she's standing. (00:00:50)
Visible crew/equipment: In Logan's apartment, when Lanny is telling Logan that Cassandra called, an orange T mark is visible on the carpet to the right of Rory. (00:05:01)
Visible crew/equipment: After Luke admonishes Sookie and takes the ladle away from her, when it cuts to Logan's dining room we can see the crew's mat with blue gaffer tape at the bottom left corner of the screen. (00:26:25)
How Many Kropogs to Cape Cod? - S5-E20
Visible crew/equipment: When Emily notices her sewing box is missing and picks up the replacement there is a mic in the top right corner. (00:34:35)
How Many Kropogs to Cape Cod? - S5-E20
Character mistake: On the first day of Rory's internship, she is told she needs to get an ID, to which she replies she never had an ID before, but she got an ID during her first day at Yale, which she and friends later pretended to lose to get new ones.
Blame Booze and Melville - S5-E21
Visible crew/equipment: When Sookie and Jackson rush out of their house because Sookie's in labor, just as Rory tells Lorelai that they should have thrown the baby shower earlier, we can see the reflection of the boom pole and microphone on the hood of the van. (00:12:35)
A House Is Not a Home - S5-E22
Visible crew/equipment: When Mrs. Kim calls Gill over to look at his van, he tells her it's not big enough for a tour van, and two tape marks are visible on the ground - one where Lane stands and one where Mrs. Kim stands. (00:37:05)
A House Is Not a Home - S5-E22
Continuity mistake: When Lorelai is talking to Richard and Emily about Rory, Richard writes down the name of an attorney and closes his memo pad but in the next shot it is open again with his pen poised.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.