I have approximately the same vintage 580D re-engined with the BT-4 Cummins-not 4x4 but extendahoe. Probably about 1500 hours on re-engine.
Brakes can be a major cost and PITA as well as loader and backhoe valve leaks. I have re-done brakes on mine and steering control valve seals. Overhauled dipper cylinder and boom cylinders-probably put 2500 into it in 3 years. Bought for 9000.
Great machines once you get rid of the for crap gauge panel that Case inflicted on these. I have dug probably a 1000 feet of water and power line trenches and moved, placed and graded 150+ yards of gravel. Love my hoe even though she痴 a bit primitive of a beast. You値l never lack for digging/lifting and pulling power- it puts the toy backhoes on CUTs and SCUTs in their place when it comes to working big or tough jobs.
All real good info, GS. I didn't think about rust; probably because it's rare to see rust here in Colorado. Don't know much about it.
And of course 4x4 doubles wear points as does extendahoe. Keep in mind that other than brakes, these old machines were designed to be built and rebuilt. They can be a PITA, but they are simple beasts. Lots of shop manuals available because they tend to age rather than break.
My buddy bought a basic 310 2wd standard of of that vintage on which everything worked ... but it needed attention to everything, too. If it had ever been serviced or even regularly greased it sure wasn't obvious. Over the past 3 years he has replaced a lot of pins, bushings, seals, and hoses. None of which kept him from getting a ton of work done with it. He even built a thumb for it! The upside is that it now works like a much younger machine. Probably worth more, too.
My own 310 hasn't been without maintenance. Something to consider is that parts & pieces are HEAVY. Even the batteries (2) are heavy brutes. When I took the boom cylinder off for new seals (it had been moaning for weeks) - it required another loader to lift the cylinder & put it into the trailer to take to the shop. BTW, the problem with leaky seals is less that fluid gets out than that dirt gets in. The seals on that cylinder were about half original rubber and half hardened clay dirt that had to be chiseled out. No, it didn't leak. Nor was anything damaged. Just needed cleaning & seals.
Like GSvette says, find a local hydraulic shop for hoses and cylinder seals. Half the price of dealer parts. Around here most every rural town has such a shop. Lots of times they are right there in the same area as the dealer. Here you can't quite throw a baseball from the dealership to the hydraulic shop - but you can see his front door from 4 different tractor dealerships - Case, NH, JD, & Kubota.
Along with not lacking power, these industrial machines are hard to bend or break. I don't know the 580 as well, but as powerful as the 310 is, I think it would stall before hurting itself. Clean fuel & filters, good batteries, a block heater, flush the coolant, backwash the radiator, hoses & belts. Just all the normal stuff. You buy a good tractor for low dollars & you gotta expect those things. What matters is that it continues working and that you keep your mind set on appreciating what you have when it's back into shape. You put any of those older Ag or industrial machines back into shape and it will last for generations of homeowner style work.
good luck,
rScotty