Apart from the waste. We really don't know what to do about it other than bury it and leave it for a few tens to hundreds of generations in the future to deal with with the hope that they will know what to do. So it's the safest option. But only for now. We might just be dooming our descendants to deal with the mess and they might be in a worse state than we are now.
I live in Idaho, and something that comes up fairly regularly is whether to accept more nuclear waste shipments to be stored at the https://www.inl.gov indefinitely. To me, nuclear power is not good or bad (it just is), but I have a very low level of confidence that humans can manage it over the long term. Power companies don't seem to be willing to spend the money needed to encapsulate waste for thousands of years.…
The "Nuclear Waste Policy Act of 1982" charged utilities a 0.1 cent/kwh fee for disposal of nuclear waste, and the DOE was supposed to take receipt of that waste. There is $31 billion in reserve for waste disposal...