The 6.0 is problematic in that it can have some problems generally fixable for around $4000. It is a requirement to keep up maintenance. Generally if you can find one without a tuner and good maintenance records you can go from there. I would recommend you go to ford truck enthusiasts web site and also the powerstroke forum. Both will give good insight on the engine and also point out what the fixes are. yes I have an 04 and spent the $4K its a good truck. My Brother in law also has a 04 and has had all the issues and fixed many. He just looked at a new truck and said he was going to keep the old one as he was not impressed with the new ones. BTW he has about 150000 on his and one of the problems was that it is a work truck and it was recommended due to where he worked that he change oil every 2500 miles; Never happened but he still runs it hard. Just put in a new intercooler and a couple of other things and said it made a difference. He has towed a skid steer on a tandem trailer so he had a good load on it and he said again no issues.
But like anything else its buyer beware. If serious what you need to do is get a scan gauge or something and take truck out for test drive to monitor the engine parameters, but you will need to go to the right sites to get them. the 2 I recommend are the best.