I agree on the chip/tuner although sometimes it's hard to tell if they've removed it. I personally will never buy a diesel truck that's been 'modded' in any way. If the engine isn't bone stock and unmolested I'm not interested, period.
What model is the truck exactly? F350, F-superduty (F450)?
Couple things that come to mind, It probably has a ZF-5 transmission. They are good but can give some trouble at higher mileage depending on how they were treated. If it runs quiet down the road, shifts smooth and the fluid looks good it's probably fine. FYI, they use ATF, not 90wt gear oil. If it's full of gear oil that's a red flag that either 1) the owner doesn't know/care, or 2) they are trying to cover up a noisy tranny. Also ask when it had a clutch last put in and if they are still running the stock dual mass flywheel. They can be problematic and come apart, generally most people swap them out for a standard flywheel at the first clutch change.
As for the engine, aside from the normal things you'd check on a higher mileage diesel (condition of the turbo, injectors, etc) these trucks also had problems with the under-valve cover wiring harness that controls the injectors and glow plugs. Fairly common problem and not too hard to fix, but can cause numerous different starting and running problems. Also check the glow plug system in general, it should cycle on with the key, Wait to Start light for a few seconds, hear the solenoids click, then should fire right up. Those Solenoids were another common problem, but again, easy to fix. Check the fuel bowl/filter assembly on top of the engine. Any leaks here can cause trouble, if they are bad enough fuel will run down the back of the engine and ruin the clutch. Last thing I can think of, these engines use a high pressure oil pump to fire the injectors. IF the truck was well maintained the system usually works fine, but it relies on a constant supply of good, clean oil. If the motor looks sludged up inside you're asking for trouble. Hopefully this helps, I'm going from memory since it has been several years since I've owned one of those trucks.