[SteveR]

If it has dual tanks, make sure the switch and valve work, they tend to break.

If it's been sitting, check to see if there is any water in the tanks.

Check the glow plugs. It's an IDI motor so if any one of the glow plugs are bad it'll be a bitch to start.

Check the fuel lines and all rubber components in the fuel system as the truck was built before they started putting methanol in diesel fuel and it will break down the rubber parts of the fuel system that are not B100 compliant.

If it's an automatic, see how it drives. The C-6 they used in those trucks tend to wear out. It's a bit hard to find a good one used as Ford used a unique case that was only used on the 6.9 and early 7.3L diesel motors. Also think about a deep sump trans pan. I hear these C-6s get real hot when hauling anything.

Look to see if the front end is sagging at all. The 7.3 is a very heavy motor and the front leafs sag over time.

I think the F-350 had the wishbone front suspension in it (my F-250 does). If so, check the tie rods. If it doesn't have a steering stabilizer, you can get one cheap.

Check the latching mechanisms in the tailgate, they tend to rust and lock the tailgate shut.

Look into getting a Walbro fuel pre-heater/water separator. It'll make starting on a cold day much easier. You can mount it to the firewall on the passenger side I think.

There should be two batteries. Make sure they're both high CCA. These motors are a bit of a bitch to start in very cold weather.