The other is that however bad those things are, or could be, global warming is still orders of magnitude worse. These very German arguments against nuclear power don't make sense at all.
Overall I'm pretty confident that in a few centuries (or even decades) people will see all of these strategies as really foolish (burying radioactive waste across hundreds of sites around the globe, dumping billions of tons of waste into the oceans, polluting the atmosphere, ...).
I have my own biases, but I am fairly confident that people of the future will come to a much different conclusion.
Every form of power generation has byproducts and waste. Many of these (even for renewables) are nasty, toxic substances. Nuclear seems to have one of the best ratios of waste to electric production of any form of power generation, including very low lifetime CO2 generation. I would hope the future people of earth are far more aghast that people kept doing things like burning coal (and then dumping the fly ash in places that contaminate groundwater) instead of building alternate sources of baseload generation.
Massive exageration by several orders of magnitude.
They say in the link you provided it is less than 126000 barrel containers of material. Even if you overestimate at 400 litres per container (they will probably be some sort of sarcophagus vessel) that is about 50k tonnes of material, for more than 30 years of operation. That sounds pretty efficient to me.
Edit: misread that you were refering to the material specifically stored in Asse II
There are ~450 reactors in the world with the US operating close to 100. You don't get to millions of tons.
Plants themselves are producing lower radiation materials, that don't need those iconic caskets or the extreme care. They wuldn't melt down or anything. This is from day to day operation (gloves, suits, containers) and decomissioning.