Sorry that was probably more hostile then necessary, but when it comes to nuclear power there is very much a "but what about the waste aspect!" used in a manner which implies all other fuel sources don't have very serious problems as well.
The law of unintended consequences has a damned long arm, that's for sure.
Perturbing systems creates long-lived ripple effects. Humans have been tapping into stored carbon equivalent to a few hundred million years of fossil deposits, and ... that's going to have some really long-lived effects. As to what the future holds, my sense is that we're simply not going to have the quantities of free, abundant, and fungible energy we've enjoyed for the past century or so. There are a few people who've arrived at similar conclusions (Dennis Meadows, one of the original Limits to Growth team is among them).
The problem with nuclear waste for me (and others -- Hyman Rickover's criticisms of nuclear energy are revealing) is that the stuff is of such a concern for such a long period of time -- literally longer than written history. How the hell do you create a warning iconography that's going to be comprehensible in 10,000 years, or even 2000? Spoken and written English of even 700 years ago (Geoffrey Chaucer) is barely comprehensible today. And structures to contain it? The very oldest intact buildings we know of are massive stone monuments and even they are both heavily weathered and have long since been plundered (pyramids and other archaeological sites).
The primary problem with oil and coal are simply the quantities we've been consuming of them. If human populations hadn't grown, and they simply substituted for the biomass which was being consumed in their stead prior to the Industrial Revolution, they'd be far less consequential.
I should try figuring out how large a population could be supported at, say, 50% of US rates of energy consumption...
See the way I see it, that's asking the wrong question: who cares what civilization is doing 10,000 years from now, if it's lost sufficient record and technology to comprehend nuclear waste?
Even a language change, if accompanied by a technologically advanced civilization, would remember to change it's signs.
Whereas, it is much more likely that if we don't use nuclear power, we'll create catastrophes that lead to that problem to begin with. I'm much more concerned with what happens over the next 10,000 years then at the end of it.
who cares what civilization is doing 10,000 years from now, if it's lost sufficient record and technology to comprehend nuclear waste?
It's possible to retain a knowledge of what nuclear waste is (at least in a mythic sense of "very bad juju") while 1) losing track of where that waste is and 2) being unable to detect or determine where it is.
Humans have no senses which detect radioactivity (one possibility is that such a sense evolves, though I suspect this is unlikely and would take a very long time). Radiation detectors require some level of technology -- silver nitrite films which fog on exposure, cloud chambers, Geiger counters, exposure badges. It's fairly easy to lose track of where radioactive products are; there's already history of radioactive decay products being incorporated into building materials and otherwise going astray (the Mexican truck hijacking this past week is only the most recent of many civilian-use accidents).
So: a future civilization, which does have a written or oral history of nuclear waste and its hazards, but no means of determining what is radioactive, could definitely have some issues going on. What the outcomes of that might be are an interesting question. It's possible there could be a civilization reboot, or humans could make a long-term slide to obscurity and/or extinction.