I just made a hay baler purchase mistake, so I think I am qualified to answer this questions.
I bought a 346 twine baler off ebay.
The number one thing to check is the bale chamber. If it has an old hay bale in it - that is a bad sign. Pull that sucker out and check for holes.
The 346 is supposed to be one of the better JD balers. The 4xx are said to have a bunch of issues and the 3x7 I am told have gear box issues.
Regardless - here are a couple more things.
Open the top access panel and grab ahold of the plunger pitman arm and check to see how loose it is.
Checking the plunger bearings is somewhat tough, but you can move the plunger to the position that on the left side of the baler you can access the left side bearing for adjusting. If the nut is readily visible - you can count on the bearing being shot.
Check the hay fingers - mine the crankshaft ended up being pretty worn. New bushings helped some - but it ain't new is all I can say.
Knotters - you need a parts list. My baler had some extra parts in there (springs).
If you know how to time a baler - that would help on the inspection. Checking the bill hooks, twine disc, etc.
Are you looking at twine or wire?
Tires, wheel bearings, pickup, pucking up teeth, slip clutch, shear bolt, needles, hay resistors, etc etc.
My baler is a 1979 model. I am getting a crash course in them - it is kinda fun.
I would say run some hay thru it or get it REALLY cheap and buy a service manual.
D.