Before saying that nuclear power isn't safe enough, consider where we get most of our electricity from today: coal. Coal may have been around a long time, but it is far more dangerous than nuclear power. The fly ash produced by coal burning often contains substantial concentrations of uranium (not too bad) and radium (very bad), as well as all sorts of other toxic but non-radioactive chemicals like lead.

Although there is a lot more net radiation coming from all the fly ash we produce that there is from our nuclear reactors, the EPA doesn't bother to treat fly ash as hazardous waste, so most people don't think it's scary. This means we already have a bunch of radioactive waste dumped into our landfills without much oversight at all.

While nuclear waste is very dangerous, there isn't a whole lot of it, and it's quite safe when it's stored properly in a radiation-sealed container. It doesn't end up in our landfills, or our air supply. It's a point source of pollution, which makes it much easier to take care of, and it is much nicer to leave future generations some concentrated, shielded radioactive waste in remote areas than to leave them tons of low-level waste in their water supply.

I'm an advocate of solar energy, and nuclear power is a hell of a lot less safe than I'd like. But as long as we're burning coal, we should be worried more about the risks of that, even though they may be less scary-seeming, because they truly are more dangerous.