At 30:20 -Luci magically appears, standing beside Helen's kitchen table.
When Elliot and Luci arrive back on the road, neither of them has the shotgun that she had been carrying earlier. It was still loaded so it is unlikely that they would have just left it out in the open scrub land.
When Ethan arrives to collect Helen from the Doctor, he attaches a steering wheel lock to the car. In the next few scenes, this steering wheel lock disappears, then reappears, as he gets back into the car.