Regarding nuclear fission energy people often talk about reactor accidents. In my opinion (and that of many others) the far bigger and yet unsolved problem is nuclear waste. Uranium-235 has a half-life of over 700 million years. We have no way to store stuff for that amount of time. I have seen no sound solution to this yet.
I vaguely remembered this from reading about it a while back but I googled it to check my recollection:
I'm by no means an expert, but my understanding is that the main radioactive product of nuclear fission (U-238) can be recycled to produce Pu-239 which acts similarly to the original U-235 used as a fuel source. This leaves only the fission products of U-235 to be dealt with which have a much more manageable half-life on the order of hundreds of years.
This is all coming from a site with a rather obvious agenda, so it would have to be double checked, but this matches with my recollection from other sources so I'm inclined to trust it.