The only "problem" that I've had with mine versus other trucks so far is the mileage. I realize it's not going to sip fuel like a hybrid, but I can only squeeze about 15 mpg on average outta this thing. My dad had an '06 Dodge DUALLY that got 22mpg bone stock!
A lot of it has to do with the addition of the Diesel Particulate Filter (DPF) in '08. Kinda like having a second cat (some more EPA crap). It collects the soot from the exhaust, and then raises the temperature of the filter by dumping fuel in it and burning it off. It usually does this every few hundred miles (more or less often depending on how hard you drive it). There's also a slight loss of power and mpg's when it goes into "regen mode" but not TOO noticeable.
Ford recommends no more than 5% bio fuel (ULSD ONLY!),
and that you not let the 6.4 idle more than 5-10 min (at the most) at a time. This is because the DPF will eventually clog, screw up the engine, and void your warranty! I think some guys here have played around with some bio-fuel in the 6.4, but I don't recall reading any results. Ford may just be screaming like Chicken-Little about the "no-idle" and "no bio-fuel" issues, but it's not worth voiding my warranty to find out.
None of these things are really problems, just some things to be aware of and think about when making a decision. Of course I can only speak for my own experience.... but other than that, I've really been satisfied with the power, styling, and quality. I don't do a lot of heavy towing like some other guys here, but it does great towing my 21' camping trailer. Sorry for being long-winded, hope this helps.