The problems were supposedly "bugs" that were addressed in previous years.

The 6.0 Powerstroke had some teething problems, like all new engine designs,
but is now a highly regarded engine.
I have an '05 F350 with the 6.0 Powerstroke. The truck and engine were a
late '04 build.  Within 12,500 miles the high pressure oil pump and
regulator (provides the actuating pressure to the injectors) failed twice,
once at 8300 miles and the second time at 12,500 miles.  They have to pull
half the engine apart to replace these.

After the second failure, I got a letter from Ford asking me to bring the
truck back in for a engine software upgrade, which I did.  The difference
was immediate.  The engine ran quieter, smoother and had more power.  I
noticed that the turbo pressure boast didn't run as high as it used to when
highway cruising or towing also.   It now has over 20k miles and runs
perfect.  I came close to giving up and trading it in after the second
failure, but I otherwise like the truck, so I decided to try again.  Now I
am glad I kept it.

The tech that installed the new software told me that it changed the
injector timing in addition to some other refinements.  Apparently the
original software caused something similar to "hydraulic hammering" of the
high pressure pump, causing premature failure.

I am sure yours has all the latest upgrades and software versions.

RCE

When we were shopping for our Excursion we were considering a used '03, but
after we found out it was a Ford buyback and got a chance to look at the
service history we passed. In the process I got a chance to talk to a couple
service managers and the two major issues for the 6.0 were bad injectors on
the first engines which was corrected in the 04 model years, and faulty
engine control software, which another poster mentioned.

We ended up getting a new '05 off a dealer lot a few months ago, it was the
last one in Michigan that was equipped the way we wanted, amd so far we've
had no problems with the engine. The front hub locks have already been
replaced under warranty, though, but I expected that...from my experience
with my SuperDuty, they'll be replaced again under warranty, then when they
fail after warranty I'll replace them with Warn manual hubs.