The problem of nuclear waste and contamination is not just a scientific problem. It is also an engineering problem, an economic problem, and a social/philosophical/ethical/psychological problem.
One problem with the scientific problem is that science is dynamic; new knowledge emerges. Levels of radioactive contamination considered safe in the 1950s are not accepted today. If current science estimates nuclear waste to be safe at some point X years in the future, will scientists at that point X agree?
Can engineers design and build a system to safely store nuclear waste across generations while keeping the total cost of nuclear energy within competitive range? Is the cost of that storage figured into the price of the generated electricity? Does the capital cost of a nuclear energy project include projections of the cost of nuclear waste storage and management across hundreds of years? How much of that cost is socialized through government subsidy? What will the regulatory environment be like in a hundred years or more? How does the total cost, including nuclear waste storage over hundreds of years, compare to systems based on other clean energy sources (e.g. wind/solar, etc.)?
Will a community (say, NY State) that wants to build new nuclear reactors also accept responsibility for storing the resulting nuclear waste across generations in that same community? Or do they expect to export nuclear waste to some other community (say, Nevada)? How will people living in these communities a hundred years from now feel about it? Do we care? Do we have a moral/ethical right to decide for them?
How does the presence of a nuclear waste facility affect the stress level of people living near it? We often hear of the NIMBY effect and sometimes it seems silly and selfish (e.g. the golf resort owner who doesnt like Wind Mills). But radioactivity is a psychologically charged topic, especially because of its use in nuclear weapons and its relation to Cancer - the Big C. It is also featured in many films from the Cold War Era, like On the Beach, and Dr. Strangelove, and has even survived to the present in the best damn Godzilla movie ever - Godzilla Minus One (watch with subtitles - not dubbed version), and of course, Oppenheimer. These are great movies because they scare the crap out of us, and that fear transfers over to our feelings about nuclear waste, which is radioactive. I would say we understand the risk better because we have been warned in a dramatic, emotional and entertaining way. If only we had a similar stream of great films warning of Climate Change, we might be better off.