what is this dohickey for?
 

Cub GT2000
I'm trying to get the underneath of my tractor back in good shape as many of the rods and levers are worn or bent and the deck doesnt want to run level.

This rod is at the rear of the deck mechanism.
According to the parts diagrams it appears to be an "Anti-Sway Deck Rod"
Does it matter that there is no washer or that the hole is buggered up?
Does the flange on the shaft need to be tight against the hole with the nut tight against the bracket?
Having not seen another new one, I don't know how much "play" is designed in.

Hazard a guess... Missing a rubber or plastic bushing? Consult the parts diagrams.

the parts diagram doesn't seem to show anything but a nut ... that hole was not machined like that from the factory so no bush will fit ;)

Does the parts diagram show one nut or two because at a guess I would say there needs to be a nut either side of the bracket shown
As it now appears it does nothing but slide back and forth through the hole
Oz

What size is the deck and year built?

That’s the deck anti-sway rod I believe. Looks like it was loose for several years and wallered out that hole. You could weld it up and redrill. I bet the threads on the rod are shot from sliding back and forth.