Fight Face - S6-E2
Visible crew/equipment: After TJ has put up the three wood shelves at the diner, when he tells Luke that the top shelf is an engagement gift just as he walks around the counter, the white T-mark is visible on the floor where TJ had been standing. (00:05:45)
Fight Face - S6-E2
Other mistake: While in Luke's diner, Luke hands Lorelai a cup of coffee in a 'to go' cup. When Luke puts the coffee in front of Lorelai, the cup makes a hollow sound when it hits the counter, obviously indicating that there's no actual coffee in the cup.
Fight Face - S6-E2
Visible crew/equipment: When George, the architect, starts walking out of the diner, the T-mark (looks like chalk) is visible on the floor beside Luke's chair. (00:28:45)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.