Is the issue of the waste really sorted out? What do they actually do with it? My feeling right now is that they´re not being particularly transparent about it...
Warning, wall of text ahead:
Well first, you have to know what spent fuel elements really are. It's not a corrosive green goo that tries desperately to escape it's container, it's a high density refractory ceramic that is about as water soluble as a coffee cup; it is made of uranium dioxide fuel pellets containing fission products and small amounts of transuranics. It is encased in highly corrosion resistant zirconium cladding. For interim storage it is first cooled in spent fuel ponds and then placed in dry cask storage built like a tank. If someone were to deliberately puncture one(with a well placed shaped charge, say) all that could happen is that small amounts of the more volatile fission products would slowly escape out into the surroundings which would be immediately detected(apart from the massive explosion it would be easily detected on radiation monitors). It would be a very costly clean-up; but the expected death toll from something like that is zero because it won't just sit around for thousands of years exposed to water.
The problem with final disposal is that it's supposed to be final. It will be sitting there for hundreds of thousands of years and if it the many barriers are defeated and some of the more volatile isotopes are transported to the surface, the small elevation in background radiation counted over geological timescales could still cause some deaths accoring to the LNT hypothesis.
Now, it turns out that almost all the long-lived isotopes are transuranics(when separated it is called TRU waste), that is neptunium, plutonium, americium, californium and curium. These are all heavy elements and by adding a few more neutrons they can all either be fissioned(fuel. Turns them into mostly short-lived fission products) or transmuted into elements with half-lifes so long that they don't pose a significant radiological hazzard. This is not possible in a thermal neutron spectrum reactor such as an LWR; you can use up some of the plutonium-239 and plutonium-241, but even numbered-isotopes tend to accumulate. There are some optimizations that can be done in thermal reactors to burn up more TRUs, but if you want to burn it all up and transmute what little makes it through to less harmful isotopes you need faster neutrons.
Fast neutrons have not been moderated by repeatedly hitting graphite atoms, deuterium atoms or hydrogen atoms until they lose most of their kinetic energy. Typically this is imagined to be a sodium, lead or gas-cooled reactor, but potentially it could also be a molten salt reactor based on chloride(enriched in chlorine-37 to avoid needless production of radioactive isotopes). See fast neutron reactor on wikipedia for a list of currently operating, closed/cancelled, under construction, in design phase fast reactors.
When spent fuel is taken out of the reactor it is so active that it must be actively cooled. It is placed in a spent fuel pool where it sits for anywhere between years to decades. After a few years it can be moved to a dry cask where it can be passively cooled.
The US government de facto forced the utilities to accept deep geological storage at Yucca mountain and charged a fee to ultimately take possesion of the spent fuel at some point in the future. I say de facto, since while reprocessing is technically legal, the investment and expertice working on the various projects were destroyed by the stroke of a government beaurocrat's pen and it's very hard to convince anyone to invest many billions of dollars into something without a guarantee that it won't happen again. There's no problem just letting the spent fuel sit in casks until the political issues are resolved.
All civilian spent fuel elements in the US are stored at the reactor site. Mostly in pools but there's some dry cask storage.
France stores and reprocesses the entire country's spent fuel from all 54 reactors at a single facility in La Hague. The waste(fission products with at most 0.1% of plutonium) is vitrified(turned into glass); the plutonium goes into MOX fuel which takes another spin through the reactor. This can go on several times before the plutonium quality degrades too much to be used in new fuel elements. This TRU waste will either have to be disposed off in a more secure design than the vitrified fission products or be reused in more advanced reactor designs at some point in the future.
Sweden is working on simular model as the US. We're charging our reactors for their spent fuel, we're taking possession of it and storing it at the central interim storage facility in Oskarshamn called CLAB. Our deep geological disposal system KBS-3 is nearly finished. The system has several barriers, the dense oxide fuel pellets themselves, the cladding, a thick steel canister inside a copper canister, surrounded by bentonite clay burried 500 metres into primary bedrock in one of the least geologically active regions of the world. The clay protects against corrosion and buffers against rock movements, if a container is cracked the clay will prevent moisture from reaching the container. After 100 000 years the level of activity is similar to the uranium ore from which the fuel was originally produced.
There is a natural fission reactor at Oklo in Gabon. It operated intermittently 2 billion years ago in an ore seam moderated by water which would intrude, allow the ore to reach criticality, turn to steam and shut the reactor off. Under what we now would consider completely unacceptable disposal conditions, non-volatile fission products and actinides(uranium, plutonium etc.) moved only a few centimeters over those two billion years. I consider this a pretty strong indication of the level of danger posed by deep geological deposition of spent fuel.
