Have your mechanic look at it.  A 2004 truck is 7 years old and subject to the same wear and tear as any other 7 year old truck,,   shocks, Ball Joints, brakes, water pump etc.

The  6.0L has a few special issue, but if it has been running good for the previous owner, it will probably run good for you.  If it has been chipped or programed, There is always the possiblity of stretched head studs.  Other common problems can be the injectors, FCIM, EGR and EGR cooler.  All can be fixed and the truck can be an excellent vehicle.

There are lots of folks on the diesel forums with 6.0L with several hundred thousand miles on them and still running strong.

If your mechanic suggest there might be some serious problems, Walking away from the $500 will be good decision. Or the mechanic report may give you the ammo to get the seller to reduce his price.  Good luck

I wouldn't panic just yet. If the 6.0 is stock and has not been modified with a chip etc, you should be fine. Most issues I have heard about occured after people chipped the truck. How many miles is on it? 5 Warranty claims for a 04 sounds low to me. I believe you can take it to a Ford dealer and ask for an OASIS report that will tell you about the warranty work (hubby told me this for you).

We have had minor warranty work done to our 1 ton dually 2006 6.0 diesel and it has been a great truck so far and is our only towing vehicle for the large LQ trailer and all the farm towing for hay, hauling tractor etc.

First off unless you have an agreement pending the truck being checked out, if you back out on buying it you lost $500.00 no question about it....

Someone posted "Have your local Ford dealer pull an Oasis report and do a carfax".  Which is fine an dandy for major history and how man time it was in the shop, but it will not help you with the service history (if a non dealer did the work) and sure will not tell you how the owner took care of the truck.

If you was around North Texas I would go check it out for you.  Or PM me and I will send you my phone number and I can tell you what to check and how to check it out a little better.  They are not near as bad as most people put them off to be....I think you are just panicking for no reason.

Does it show what the 5 claims are on the oasis report.  These could be little things like reflash the FICM, egr valve, a door rattle or even the power peddal needing adjustments. 

 I have an 03 f 250 with 6.0 and have been pleased with it's performance and reliability. I did have to replace the high pressure oil pump last year but no other problems

If the price is right I would still buy it.  Out of the things you listed for warranty work, most are pretty much one in the same.  The injectors FICM wiring and rough idle all could have been just one of the items causing the problem but warranty does not pay very well for a wiring harness, but will pay good for the injecotors.  The Dgas bottle is very common and could have been broke while working on the injectors.

The accident report could be something as simple as a bumper or windshield cracked. And this truck showing 3 owners, since you said it was in Texas and now nother state I would say it had just 2 owners. 

Anytime you transfer a title to another state Carfax/Autocheck records another owner.  ie: If I was to move from Texas to Ohio with the truck that I bought new in 08 as soon as I transfer it to Ohio and get an Ohio title and tags it wll record another owner even though I still own it.