Hi and welcome to diesel ownership.
I don't know who suggested that the diesel engine is prone to problems because it's pretty near bulletproof and far less temperamental than the V6 petrols. The caveat will be the competence of any previous owner just like it is for any old used car. There's nothing particularly special to worry about other than not letting the fuel tank run too low (1/4 min is safe). Oil change with decent 10W40 every 5K miles, filter every 10K and otherwise follow the GM servicing schedule and it'll just keep chugging along.
You might find some of the oil seals are getting a bit weepy, a good reason not to use thinner oil, which the engine doesn't really need anyway, and a job that can be gradually sorted out bit by bit.
Problems will be due to age/natural wear and tear, poor ownership and poor quality workmanship. Standard lottery really.