My '05 6.0 turned 80K today pulling a 24'x6'8" steel stock trailer, loaded up, like it usually does. It's never missed a lick, and I'm very happy with it. The '03 6.0's were the most problematic, and they got progessively better through the years. Chances are very good that if it has not been modified (chips, tuners, cold air intakes, etc...) or abused and has been well maintained that it's fine.
There's an easy way to find out, though - get the vin number of the truck you're considering and go register at www.ford-trucks.com/ , then go to the 6.0 liter section of the diesel forum and find the Oasis request thread, post the vin there, and one of the members will get you a copy of any work that's been done on it in any Ford garage anywhere. They'll also help you interpert the results - it's actually good if certain things have been already resolved on certain model trucks, but for the most part, the fewer results the Oasis reveals, the better. Lot's of other good info there as well. I'm sure powerstroke.org has much of the same good info, and may be able to get you an oasis, too. In any case, these sites are worth a look.
Good luck.