Visible crew/equipment: When Rory is finally going back to Yale, in the scene where she and Lorelai are standing by the car debating who Paul Anka likes better, Rory gets in the car to drive away, but in the next shot of the car actually driving away, you can see what is a man's arm driving the car. (00:06:50)
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)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.