We have a fleet of superdutys at work. On a 99 I would look at the underside of the rocker panels and the 1st and 2nd bed crossmember. That's where they seem to start to rust first. (Of coarse the rear wheel wells to, buts that's usually obvious.) The body mounts start to degrade and fall apart. The rear doors on a supercab... the lower latches seize or the spring breaks and they won't latch properly.
The shifter tube in the column seizes or cracks and it won't shift fully into park or low gear. The OD switch wires rub on everything in the column and wear through. (Obviously not with a ZF, but that's for anyone else who may stumble across this in the future.)
The front axle (assuming it's a 4x4): The u joints like to seize up (both the axle shaft u joints and the front of the front driveshaft have been the most common). The rear mounts for the front springs go bad and cause a nice clunking noise over bumps. The track bar mount at the axle end likes to break. (Usually on the trucks with plows or regularly get overloaded.)
Engine: It's a 7.3... they leak from everywhere. Most common issues, the IPR goes bad or the cam sensor. They're good for injector harness issues, injector stiction, or leaking oil everywhere.
Trans: out of the 100+ F250/350s we have, only one has a manual. It's in a garage kept '97 F450 with 7,000 miles... no issues. (It's a spade truck, used to dig out trees and root balls for transplanting. Hence the low mileage.). I've found that it's not uncommon for the trans mount ears to rot right off the case.
Rear axle: check the shackles for rot. Check the springs for rust jacking. (The leaves will actually start to bend away from each other and snap.) The parking brake shoes will fall apart inside the drum or the retainer pins will pull through the backing plate. (It's disc service brake with small drum parking brakes.)
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