Overall, they are a very good engine. They had very little common problems. For the volume of the trucks on the road with this engine, I would say it is one of the least problematic engines out there. There are things to go wrong though, nothing is trouble free.
Some things to look for are:
Leaky fuel pressure regulators (super easy to replace yourself)
Leaky exhaust manifold gaskets/cracked exhaust manifolds (you can hear this on a cold start)
Leaky passenger side head gasket (external leak which is visible from under the hood at the front top corner of the gasket (somewhat expensive repair but not real common)
Leaky intake gaskets (they only leak air, not coolant. This will set a check engine light when they leak)
Water pump (this is to be expected from any engine eventually)
Again, for the volume out there, they really don't seem to have a high failure rate with any of these items.
Hope this helps.