I lived in a concrete slab home in the 70's and I found that the biggest problem was that if you had a plumbing problem, you would have to tear up the concrete to get to it.
One of the major problems is that the slabs were not built on solid ground and they may be giving away. As the ground gives away over the years it will cause the slab to break up and eventually it could lead to major problems that would need some attention.
