Follow the link in the Wikipedia page to the article on reprocessing. It solves both of the issues you raise: it greatly extends the time the fuel lasts, and it greatly shortens the time that the remaining waste is dangerous. The only reason this was even an issue in the US (it isn't in other nuclear-using countries) is that the Carter administration banned reprocessing because of misplaced concerns about proliferation. In March 1999 the Clinton administration finally reversed that position (probably because it was obvious by then that reprocessing didn't increase proliferation risk--every other nuclear-using country has reprocessed its fuel from the beginning and there have been no incidents). So we can just take all the stuff that was supposed to be stored in Yucca Mountain for 10,000 years and reprocess it instead. Problem solved.

I don't believe reprocessing means "no waste" but anyway, that's just half of the problem: what will we do in 50 years ?

And how do you reprocess the lives of the 200'000 people who had to leave after the nuclear accident in Tchernobyl alone ? Tell the fishermen by Fukushima to go reprocess their lives because some over-confident engineers thought they mastered what they were doing.

Nuclear power is just like the "green revolution": pure megalomania by people too afraid to consider alternatives like... a less power greedy way of living.

I didn't mean to imply that reprocessing meant no waste: it means a lot less waste, that needs to be stored safely for a much shorter time. Also, since it allows you to use the fuel much more efficiently (without reprocessing, only a couple of percent of the usable fuel actually gets used; the rest ends up mixed in with the waste and is just stored without being used), it does solve the 50 year problem as well.

That said, I also didn't mean to say that we shouldn't consider all the impacts of nuclear power. But, as many others in this thread have commented, to be fair we should also consider all the impacts of other power sources as well.

As for a less power greedy way of living, I'm all for it, as long as I don't have to give up actual functionality. I'm all for having more efficient cars, but I'm not going to give up having a car; the freedom it gives me is too valuable to give up. (And no, living somewhere where I don't need a car to have that freedom is not an option. Been there, done that, prefer not to. Not everyone wants to live in that kind of environment.)