Going from my experience when I picked up a used 580E. Service records are a good place to start. Absent those, all the obvious stuff; water in the oil, water in the hyd. reservoir, cylinder leakage / bent, self leveling linkage, slop in the controls, tire wear. Then find some heavy stuff. Fill up the front bucket and try lifting it. Outriggers, found a bad pin holding the pad on, cracked through. For the B/H, we chained up an old 4 cylinder diesel, lifted and extended (finds leakdowns pretty quick). Check for cracks and welds on the lift arms, boom, etc. One aggravating thing lately is that the shuttle shifter creeps into reverse when using the B/H. The detent on the steering column is getting rounded out. So until it's fixed, every now and then I have to reach around and put it back into neutral. This list should help get you started. I'm sure the others will help lengthen it.