Sounds like a smokin' deal to me - I paid $8000 for my 580B 10 years ago, and it wasn't in that good a shape.
There are two subframes, one on each side, that bolt to the tractor frame - so that's a possible wear point. Then, the hoe frame has a 4-point mount - the two lower pins can wear in their bores in the frame, plus those pin sit in half-moon shaped cutouts in the subframes - another wear point.
The upper pin mounts are a bit more tricky - coming up from the axle area on each side are two clevises, which thru-bolt thru upper swing arms - there are 1-1/2" nuts/washers both above and below these swing arms.
If there is slop in the upper/lower mounts, (or just for R&R of the hoe) here's the procedure -
Clean the threads of the clevises, wire brush works - spray Liquid Wrench or similar around the nuts so they'll wanna move a bit easier - then run the lower nuts down and AWAY from the swing arms maybe 1/4" or so-
Then torque the upper nuts down onto the swing arms, to 250 ft lbs.
Run the lower nuts up against the swing arms, just snugly.
Now torque the upper nuts to 450 ft lbs. (This is NOT a typo)
The older CK's used two short pin/bushing mounts between the hoe tower and boom (2 pins, 4 bushings), and the hoses ran between those two clevis-type pins/bushings - parts for those are basically non-existent now, but you can buy a kit with SINGLE pin and repair bushings - if you have slop THERE, do NOT buy/make new hoses til AFTER you fix the bushings -
I did that on mine, and now I have to REDO hoses after I do the bushing repair. The one-piece pin passes thru RIGHT where the hoses go, so each hose will need to be 2-3 inches longer so it can pass OUTSIDE that full-length pin.
Here's the repair kit for 580B and C, I'm not sure about the original CK (Construction King) -
Equipment Parts Source, Aftermarket, Case, Backhoe, Crawler, Loader, Dozer, Tractor Case Backhoe Pin Kit
Those guys have pretty good prices on cylinder re-seal kits too.
You may have noticed that your toolbox is gonna need bigger drawers unless you already have wrenches up to at least 1-1/2" - you can keep the 4 foot cheater pipe somewhere else
... Steve