To be frank - nothing. The only real issue with them is not that they are "bad", but just old. And like everything that ages, it deteriorates and need updating over time. But when it comes to drain lines, most of the deterioration that happens goes unseen until something becomes a real problem. What problems specifically?
Two come to mind right off the bat - too thin and too thick. Let's talk about the "too thin" part first. As cast iron pipes age, they generally develop tin spots in the pipe walls and develop pin hole leaks that either slowly drip, or let out a gush of water one day. The too thick aspect has to do with the buildup of material around the walls that restricts water flow over time. Since this goes unseen, it can make a real mess when it becomes apparent. So keep an eye on those cast iron pipes.