Visible crew/equipment: When Lorelai and Rory walk into the living room while Emily is on the telephone with her lawyer, the filming equipment is visible at the right side of the screen. Then when Emily walks over to the bar to pour a drink, the T-mark (looks like chalk) is a bit visible on the floor where she stands. (00:00:25)
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)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.