You can't simply tune DOD out, you need to block off some passages and change the lifters. A couple common issues is not only burning oil but I have seen quite a few with stuck DOD lifters. If I was buying one, and I plan to in the next couple years, I would go all the way with the engine changing lifters, tuning, and deleting DOD.
It is also common to see failed fuel pump flow control modules, they either fault, or stop working all together keeping your fuel pump from turning on. There has been a policy that covered some but not all of the effected trucks.
The EVAP system tends to burn up vent solenoids, and the replacement parts require rerouting of the system.
The front diff tends to leak at the axle seals, and I have also had to rebuild a few of these, although they typically last to 100k or more so long as they are taken care of. A failed front diff seems to be common in trucks that see a lack of maintenece and it's the first thing to fail.
There are lots of other stupid minor stuff, the bowtie emblems suck and look horrible in a short time. The power folding mirror option breaks, and you have to buy the whole mirror assembly from GM to fix it. The uplevel interior (LTZ) has problems with chrome pealing off parts. The 3rd brake light is prone to leaking water if it's removed to replace a bulb. I have had to replace rusty rear bumpers before they were out of warranty. I'm sure there are a few things I'm forgetting.
Now I do like the seats, and I think they ride pretty well for a truck. They are not very hard to work on (maybe I'm biased because I do it everyday). The drivetrain aside from the DOD is very reliable if taken care of, fresh fluids every couple years, and lack of abuse will keep it going for a long time.