In areas with heavy coal mining activity the water and the soil is poisoned from erosion and runoff and people that live in these places come in enough contact with the toxins (mostly heavy metals) that they develop medical problems later in life. In practice the effect is about the same that you'd get if you lived in a radioactive area.
This is a non argument. Nobody is seriously proposing coal as an alternative to nuclear. Sure in some countries (e.g. Germany) they phased out nuclear before coal, but there are very different reasons for this, for example they are favoring brown over black coal. That is for different reasons though, largely the political lobby and associated jobs in economically weak regions (note I'm not saying this is right).
However, nobody is proposing coal as a long term solution. Yes one might make the argument that nuclear is safer than coal (however that argument is by no means as clear cut as you make it out too be), but the competition are renewables and neither nuclear or coal come close.
Not the parent, but if you look at what's currently replacing nuclear power world-wide it seems to be gas. Gas extraction is also not very environmentally friendly and releases a lot of nasty toxins into the air and surrounding areas, just not as much as coal mining does. I think the point still stands.
