Typically the 05-07 6.0L's have the following issues (and be aware that at the mileage you are looking at, some of these issues may or may not have already been addressed):
HPOP STC fitting prone to failure (one piece fitting will address this).
Dummy plugs and standpipes prone to leak - updated parts will address this. Late 04's have these issues also.
Weak fuel pressure regulator - updated regulator spring will fix this. All 6.0's have this issue.
EGR cooler prone to leak - BulletProfDiesel makes an EGR cooler that won't leak, or install a good EGR delete. The late 04's have this issue also.
OEM coolant (all years) is prone to gelling with excess heat, when mixed with other coolants, if exposed to combustion gas, or if not properly maintained (30-40k drain/flush/fill intervals). This gelling WILL plug the oil cooler and problems will "domino".
OEM FICMs aren't tolerant of low voltages and can fail often (all year models). A 190A (Leece Neville makes a good one) or higher alternator is highly recommended. Also, getting upgraded components installed in your FICM is highly recommended. FICMrepair.com is the best place to help you with these issues. Good batteries are a MUST! I like a quality AGM battery (Odyssey's are expensive but the best I know of).
Brakes and suspension are better for the 05-07. The upfitter switches are also a nice feature not available on the earlier model years.
05-07's also have some nice injector and turbo upgrades.
Coolant filters are good mods, but even more importantly is to use a good coolant. Switching to a name brand CAT EC-1 rated ELC coolant is a must. A proper flush is required for best results. Most shops won't take the time for a proper flush, so this is a DIY project. Lots of forum threads on this.
Ultimately, you would want a fuel pressure gauge installed. Low fuel pressure (45 psig or less at any time) can damage injectors. At higher mileage (200k miles +), injectors may be required before too long anyway. If they have already replaced injectors, find out what they bought and from whom. The best injectors (unless you are going bigger) without a doubt are OEM remanufactured injectors. Sometimes low fuel pressure can be a weak regulator spring, plugged fuel filters, excessive water-in-fuel or dirty fuel, weak pump in the HFCM, etc. Might be a cheap fix or might cost $400 plus.
Be aware that 03 and 04 model years have a weak HPOP (fairly expensive), but they are not as prone to leaks in the HPO system AND they have a fairly strong EGR cooler. Also, the 04 model year is a transition year. The 04's have 3 different versions (early, middle, late) that can affect what parts you buy. The forums pretty much have the major parts issues and requirements well documented for the 04, but even for dealership parts guys can have trouble getting the right parts.
03's and even 04's are prone to wiring harness issues and generally have more sensor problems than 05-07 (ICP sensors and harness especially, but also EBP sensor).
Lastly, the 04 and 05 Excursions can be somewhat of a parts problem as well. Seems Ford dumped in older parts into these trucks to work down excess inventory.