Drew,
Early on, there were issues with the injectors. By now, most, if not all of them have been pulled out of service under a warrenty repair, or posibally a truck buy-back. I have read that Ford did buy-back some very troublesome trucks early-on. Some of the early trucks would shutdown without notice, and not refire. Unfortunatly I have read this also happend in the 6.0 Equipped ambulances. I don't think I need to explain what happend there....... yes just what you are thinking......
There are/have been issues with the Turbo and EGR Valves. If the trucks are not driven much, or are driven easy, long idle times, the EGR Valve and/or the veins in the turbo can stick. A 6.0 loves to be worked...... don't drive one like a grandma.......
The EGR Cooler can leak, this is a symptom, but not the actual problem. What causes the EGR Cooler to leak is: The water flow passes trhought the oil cooler, and then into the EGR Cooler. Contaminates in the coolant can begin to plug the oil cooler, which starved the EGR Cooler of coolant. The EGR Cooler can be "super-heated" to the point it can cause the solder in the cooler to melt, which causes a leak. There have been alot of EGR Deletes done because of this issue.
Head Gasket issues. The 6.0 is "turned-up" factory by Ford. The VT365 (IH Version of this same engine) is sold by IH at ~275hp. Ford sells the 6.0 at a stock 325hp. This is pushing the engine closer to its design limits. The addidion of "power adders" chip/tuner/programmer, further pushes these limits. This can cause the head gasket to fail. Now, just to clairfy and to help avoid being flamed on this, just bacause a power-add is used, does not automatically mean that a head gasket will blow. The have been owners that have successfully used programmer without issue, just as there have been owners that had head gasket issues on a 100% stock engine.
Now do not let this list scare you away. Each of these issues can be rectified, and make a fairly bulletproof engine. EGR Delete, Head Studs..... but there is no reason, if you buy a 6.0 to take it home and tear it down to do these items.
Here is my experience. I own a 6.0, in a 2003 Excursion. It currently has 108,000 miles. I have the factory EGR Valve, EGR Cooler, Oil Cooler, Turbo and head gaskets. I do let the truck idle some. This truck has never left me stranded, and is my "family car". I do not hesitated to load the "boss" and 5 kids into the truck and go anywhere. The onl issues I,ve had is alt/battery issues, which is not the fault of the engine. But, I am 100% stock. The only modification is the addition of a FUMOTO Oil Drain Valve. The only work that I've had to do is, brakes, tires, oil changed, fuel filter changes and feed it #2. I have a set of Bilstein Shock at home waiting to go on this weekend, thank to a crater I "found" last week. I have looked at many other trucks, and I would buy another 6.0 without hesitation. I know there were issues, but most have been worked out. This has not scared me away from them.
All engines have their quirks. Look back throught the history of just the Diesel Engines in the Ford Trucks:
6.9 IDI - Early engines could crack around the block heater if the heater was used, and weeping headgaskets were not unusual.
7.3 IDI - Cavitation...... preventable..... but deadly to the block....
7.3 PSD - Yes the "ultimate best diesel". Cam Position Sensor, can put you on the shoulder in a heartbeat with no warning. HPOP System Leaks, VCG/UVWH..... no flaming please, just stating facts...
6.0 PSD - EGR Valve/Cooler, Head Gaskets, Turbo.
6.4 PSD - DFP, causing reduced fuel economy and other related issues. Not the engine specifically, but any major repair on the engine the cab has to come off.....
6.7 PSD - Jury is still out.... but it has a DPF plus has to run DEF, so higher operating cost.
I know not diesel, but the infamous spitting of the spark plugs in the earler 5.4 and 6.8 gassers.....
I would say if you find a good solid truck that has not been thrashed or "hot rodded" (I know relative term) you should be ok. Just my opinion from my personal experience.