Long story short it's an acceptable risk. Accidents are going to happen, people are going to die, the land and air will be poisoned, absolutely. That's the price of doing business and that's nothing new.
Exactly. As has been said many times already, it's pointless to demand that nuclear power, or anything else, must be absolutely 100% safe, because that's simply never going to happen. There's always going to be risk, some that can be foreseen and mitigated to some extent, some that we won't even think of until it happens, and some that we wouldn't be able to do anything about anyway.
What's important, as with pretty much all aspects of life, is the risk/benefit analysis. I think part of the problem with this is that most people don't seem to realise they actually do that all the time. Every time you cross the road, you're weighing up the benefit of being on the other side with the risk of getting run over. It's no different when it comes to electricity, just a different scale.
Of course, another part of the problem is that people are absolutely terrible at actually assessing risks and probabilities. Which is particularly relevant for nuclear power since a large part of the controversy over it is due to the irrational fear many people seem to have of anything involving the words "nuclear" or "radiation".
In the end, all you can do is point to the facts. Nuclear power - in 50 years less than 100 dead, and a few thousand projected deaths at most, some economic cost, virtually no environmental cost (the Chernobyl area has actually been claimed to be healthier due to the lack of humans, although those claims have been disputed). Coal power - tens of thousands directly dead, far more by indirect routes, massive environmental cost including such fun as smog, acid rain, and
deadly clouds visible from space. Note that I don't even need to mention global warming, coal power would still suck even if global warming could be conclusively proven not to exist.