I didn't say that there aren't concerns and it is indeed right to be wary of the risks and dangers. I recognize that this was a comedy show, but let me give a couple of simple examples of why it displays complete ignorance of the subject and only serves to scare people. I'll only give a couple of examples.
Half-life of Plutonium - PU-239 has a half-life of 24,000 years as stated in the video. But what does that mean? It is generally considered to be five half-lifes and the original material is considered effectively gone. So is that roughly 125,000 years before Plutonium is gone and safe? No, that's just how long it takes to naturally decay away (let's ignore the daughter products for this discussion).
There are six primary isotopes of Plutonium, five of which naturally decay away via Alpha decay (a Helium nucleus) which is has a very high electrical charge (+2). The high electrical charge means that it requires a very special type of shielding to protect living things such as a piece of paper or dead epidermal skin or any article of clothing.
The sixth decay method is via a beta decay (a proton or electron, in this case an electron), which is also electrically charged & shielded in a similar manner as an Alpha decay particle.
The video then immediately goes on to discuss "if ingested" which has nothing to do with the half-life that they just discussed. Plutonium is far more toxic causing heavy metal poisoning then the risk of radiation (unless ingested or inhaled, inhaled being worse). A long half-life is often considered to be a "stable" isotope since it has few radio-decay events, but that never discussed.
There are a lot of isotopes which exist naturally with very long half-lifes that are not dangerous such as Potasium-40 (1.248x10^9 years yet no one discusses the dangers of bananas, avacados, yams, or potatoes), Carbon-14 (5,730 years, hence carbon dating technique)
Similarly Granite (countertops?) have naturally occurring impurities of Uranium (U-238 is over 99% of all naturally occurring Uranium and has a half-life of 4.468x10^9 years with alpha decay but it isn't considered a hazard to put into kitchens with food preparation) and Thorium (also crazy long half-life).
Storage - This is definitely an issue, but one that is far more plagued by politics than technical issues. There are different types of waste which require different solutions (i.e. spent fuel vs. irradiated reactor components like Cobalt-60 vs. secondary items like reactor water chemistry test samples). If we activated Yucca, then there is the politics of transporting the waste to the site and every political jurisdiction playing politics.
Mistakes were definitely made in the past but there has also been significant technical advancements. Metallurgy is better for containers. Non-destructive testing for quality controls and quality assurance in containers for fewer faults which could leak. There have been theories not fully investigated such as actively irradiating waste in order to speed up the decay process significantly and render the material radioactively inert in much less time.
Unfortunately, as it is, people are not properly educated about it other than "radiation is bad". Most people do not understand the difference between "radiation" (and the various types), "radioactive" (e.g. bananas are naturally slightly radioactive because of the Potasium), "contamination", "radiation leak", "half-life" nor the difference between the hazard due to ionizing radiation and the toxicity of the element (i.e. Mercury or Lead). However, you can be assured that there is plenty of false information spread by people who incorrectly use those terms interchangeably
