Use the second nut or not, it doesn't matter. DO NOT put a nut between the washer and the chassis. The washer is there to isolate the jack from the chassis, putting a nut there could create ground loops.
To check your jack, measure the resistance between the center pin and the ground tab. If it measures very low, the jack needs to be replaced. If it measures very high/over limit, it is fine ton use but may fail at some point down the road.