My uncle once explained to me that the really hard problem of nuclear waste storage isn’t designing a facility that won’t leak, it’s designing a sign warning future people not to let the waste out. Probably the easiest way to grasp the challenges involved is, as Juliet Lapidos says, to think about ancient Egypt:
The tomb of the ancient Egyptian vizier Khentika (also known as Ikhekhi), for example, contains the inscription: “As for all men who shall enter this my tomb … impure … there will be judgment … an end shall be made for him. … I shall seize his neck like a bird. … I shall cast the fear of myself into him.” It’s possible that the vizier’s contemporaries took Khentika at his word. But 20th-century archaeologists with wildly different religious beliefs had no reason to take the neck-cracking threat seriously. Likewise, a scavenger on the Carlsbad site in the year 12,000 C.E. may dismiss the menace of radiation poisoning as mere superstition. (“So I’m supposed to think that if I dig here, invisible energy beams will kill me?”) Hence the crux of the problem: Not only must intruders understand the message that nuclear waste is near and dangerous; they must also believe it.
The good news is that insofar as we manage to avoid a major civilization-collapse and the attendant loss of knowledge, future people will probably be able to figure out that the danger is real. And if we can’t avoid a major civilization-collapse, then the collapse, rather than the post-collapse nuclear waste incident, is the really the main problem.