Biggest problems as I see it would be ventilation and the possibility of a cave in. Building any kind of structure that requires tunneling, or even working within a preexisting cave or tunnel is tricky business and you really have to know what you're doing. Also as I said ventilation is an issue, there is a possibility of poisonous gas buildup and the air will get pretty stuffy down there even without it. You'd definitely need some sort of mechanical air circulation system if you wanted to actually live down there, as mines tend to be quite deep.
Frankly mines are pretty unsafe places to be even for actual miners, who are paid well because it is pretty dangerous work. Old abandoned mines I imagine are even more dangerous. If you were actually serious about creating a permanent dwelling inside one it would probably require a lot of structural work, steel support beams and concrete walls and the like, plus you would probably need a geologist or some other sort of expert to examine the place before you build anything. Like I said digging underground is tricky; if you make a hole in the wrong spot you can literally bring the whole place crashing down on top of you.
Realistically you would probably end up spending a lot more money than you would if you just bought a cheap piece of land and built a house on it, like possibly millions of dollars. I would say if you were wealthy and really wanted to do it, it could probably be done, but if you're just looking for cheap off-grid living it's far from a practical option.