[COLOR="Blue"]What exactly does this part do? [/COLOR]
During wash cycle, water is pulled through the screen filter at the back of the tub and then through the valve and back up to the spray arms.
During drain the valve seals so that the water is directed out the drain instead of back into the tub.
The normal symptom for a bad Piston & Nut is incomplete draining.
Since it is shot I would replace it.
Though I doubt it is causing your problem.

Poor wash results can be one of the following:
1. Food bits/junk is clogging some of the wash arm holes.
2. Something impeding the wash pump. Remove the sump cover and check inside the sump for debris or something wrapped around the chopper. Be careful there is often broken glass in the sump. Also note how the inner piece is installed, put it in wrong and the chopper will eat it.
3. Low water level. Most units should fill to just under the heating element.
Often the pump will be noisy with a low fill as it sucks in air. Often this is just a partially clogged inlet screen filter on the water valve.
4. The heater is not working for some reason.
5. The water entering the machine is too cold, should be a minimum of 120 degrees F.

There are other possibilities but the above are the most common.