Nuclear energy is "cleaner" in the carbon emissions sense, is heckof energy dense, is damn expensive, is here now and growing, is a viable and practical solution to climate change.
There are many ways to do it better: it is theoretically possible to separate the really nasty million-year-half-life stuff and recycle it into a few hundred-year-nasty stuff, getting more energy out in the process. You can better safeguard and better safeguard, and I bet we have the ability to get our safeguards pretty darn goon.
But I am reminded, over and over again, of the phrase "anything that can go wrong, will go wrong." And nuclear, just being what it is, can go pretty darn wrong. Yes, there are safeguards upon safeguards. Yes, waste can be managed--although we are not doing a particularly great job at the moment, due purely to political limitations. We're a heck of a lot better at overcoming technical limitations than we are at overcoming political limitations.
But you know, that Deepwater Horizon blowout preventer was not supposed to be able to fail, either. Something going terrible wrong is always within the realm of physical possibility, and in the case of nuclear the consequences for life on earth are really serious business.
Right now, this burning of fossil fuels thing is potentially going wrong for us, and we're gonna run out eventually anyway. So in a cost-benefit analysis between a climate that is definitely warming up and changing even if we still don't know how much, and a remotely possible local but who knows maybe worldwide radiation induced horror, which would I choose?
Honestly, I'd choose a warmer climate.
(But Science! is still good at what it does, so let's keep doing it re: nuclear fission processes that are safe. Keep the physicists employed!)