Sarah, The 6.0L as they age have had a few common problems.

FICM ( Fuel Injector Control Module)  This is usually some solder joints become weak and you have loss of voltage. I think a new module is $400 $500. But there are several threads on the Diesel websites that  give directions on how to pull the module and resolder the weak connections and how to test.  So if you do it yourself, It's an afternoon for hubby. If you take it into a dealer, it will be the $500 in parts and half a days labor. So $800-$1000

http://www.thedieselstop.com/forums/f50/detailed-ficm-repair-procedure-244155/

Mine went bad at 90,000 miles

HPOP  The endcap on the High pressure oil for the fuel injectors has a tendency to leak.  When it does, the dealer needs to pull the valve cover and rebuild that part.  I had mine done at the same time as my FCIM. The bill would have been $1800 for both. But since i was under 100,000 miles and 5 years. The warranty covered it.

EGR  The egr is a $400 repair if it becomes plugged

EGR Cooler.  This is cooler that cools exhaust that is being recirculated back into the engine.  The part itself isn't terrible expensive, But you have to remove a lot of components to get to it. So the labor cost get expensive.  I never replaced it on my trucks, But it seems to be a common topic in the repair forums for the 6.0. I think if you are going to drive that truck to 200,000 miles, It's probably something you will see along the way.  Here is a detail explaination of whats involved and an aftermarket replace part. http://www.bulletproofdiesel.com/Articles.asp?ID=146

If the truck has been chipped at. Head gaskets seem to be at risk.  The common repair is to replace the head studs with those that will withstand more pressure.

I use my trucks hard.  they have some sort of a trailer hooked up almost daily. They do lots of short trips and start and stops. All in all, I was happy with my trucks that had the 6.0L. The 6.0L is a little weak when trying to get rolling from a stop with a load. Thats why ford went to 6.4L and now the 6.7L  to give them a little more umph.  There were a few minor problems, In my case they were repaired under the 100,000 mile warranty.  I did pay for the following

2nd gear silenoid  About $700 at about 70,000 miles

Clock Spring in steering wheel $200   at about 80,000 miles

Speed sensor in rear end  few hundred dollars at about 40,000 miles

I went thru 4 glow plugs.  They are $29 a peice, But $200 to open valve cover to install. The dealer swears they rarely ever replace any glow plugs on other 2005-2007 6.0L.  In fact he claims they only keep 2 in inventory because they replace them so seldom.

2003 to 2007 are pretty much the same engine.  The 03 and 04 being the best for least amount of egr problems 05 being worst of the bunch for turbo problems.  Just like ANY engine there is issues with all of them.

If the truck is priced right I would buy it in a heart beat.  The biggest issue with these engine while towing is the egr and egr coolers which about $300 to $600 bucks or so plus labor (if you do not do the work yourself) can fix for good.  The FICM can also cause rough idle issues but mainly on 03 to 5 models. 

Best way to check for egr troubles before you buy the truck.  Remove the coolant cap and check for signs of oil or diesel by smelling of the cap and looking into te tank.  If is smells like anything but coolant either pass it up or call me and check it out further and offer them a big cut on the price and fix it.  I am working on a 05 4x4 F-250 right now that haa/ had egr troubles and I am fixing it the right way so there will never be an issue with that part again.

The only real issues with the F-450's was the ones with 4.88 gears starting making rear end noise around a 100-k and this is a $1000 fix.  The trucks with 4.30 gears was just fine.

I have an 06 6.0 and it has been a relatively trouble free truck. Right after I purchased mine, I took it to be checked out by a friend of mine (Ford diesel mechanic). They "fixed" (deleted) the EGR cooler, replaced 3 sticking injectors, replaced the oil cooler, and rebuilt the turbo. The truck was under warranty so the injectors, oil cooler, and turbo were covered. I have done several low cost things to ensure this trucks reliability.

Something else you may want to check besides the coolant is the oil. Make sure it doesn't look like chocolate milk. Thats a dead give away for headgasket issues. Also look for white flakely residue around the coolant cap. It would look like it spewed out. That can be a sign of EGR cooler/Oil cooler problems and usually headgaskets are next in line.

You can call any Ford dealer and have them run an "oasis report" on the vin #. This will tell you what warranty work has been done to the truck which will be a pretty good indicator of whether it is a problem engine or not.

 As for being a towing disappointment vs. the 7.3, I will get flamed for this, but my opinion is that the 6.0 pulls better than a 7.3. The 6.0 is an amazing engine and the later years (06-07) had less warranty claims than any years of the 7.3. (I'm not saying its a better engine-thats a longshot, I just don't think people give the 6.0 the credit it deserves.)

I agree with you 100% on the bold statement!  Too many people jump on the bashing band wagon because they "heard about something or a friend of a friend had trouble"  Very few actual real time owners bashing.....

The first part of the quote I have to ride the rail....  I have used some bone stock 6.0's that would hardly pull our 10'LQ 3 horse Sundowner but had a couple that would pull the hitch right off of the trailer (in stock form)  But on the other hand after deleting the egr and egr cooler then adding exhaust/air intake and mild chip or programer I would put any of the 6.0's agaist any of the 7.3's on the road.

[\QUOTE] The first part of the quote I have to ride the rail....  I have used some bone stock 6.0's that would hardly pull our 10'LQ 3 horse Sundowner but had a couple that would pull the hitch right off of the trailer (in stock form)  But on the other hand after deleting the egr and egr cooler then adding exhaust/air intake and mild chip or programer I would put any of the 6.0's agaist any of the 7.3's on the road.

Fair enough. You have a much larger experience with them than I do. I should have put the disclaimer "based on my experience."  With mine having the EGR cooler and valve deleted and a SCT tuner (with a very mild custom towing program-mainly for the "turbo brake"), it will rock and roll. I'm itching to get my headstuds installed.

When we go camping, we caravan with about 5 big LQ trailers. 2 7.3's, 2 6.0's and a duramax normally. They are all great trucks with good engines. We don't pull fast so they all do everything we ask and nobody has had too much trouble.  

YEAH, You and me both....  I love my Dodge with the 6.7, but if I could ever find a F-450 or even a F-550 with the 7.3L engine in a crew cab truck I would buy it in a heart beat.  Heck I have even been looking at the XL package work trucks to fix up but most of them are torn up pretty good on the inside and dents all around the outside.  Don't mind doing a little work but in and out I will have to pass.

Good luck on your search.