Exceprt from the blog:
Second, it's extremely difficult to destroy plutonium effectively (some weapons are built out of highly enriched uranium and that can just be diluted in U-238 and used for reactors). Obviously, you can melt it down, but that just leaves you with a chunk of subcritical plutonium which someone can re-form into a new weapon. The plutonium is highly toxic, so you can't just grind it up and scatter it around without causing huge environmental impacts (watch Chernobyl if you want to get a sense of what I'm talking about here). You can't burn it because then you're going to have oxidized plutonium in the air, which you don't want people inhaling, and while you can of course use chemicals to dissolve it, vitrify it, etc. you're still left with an equivalent amount of plutonium, just bonded to some other stuff, and so it's just a matter of (potentially highly unpleasant) chemistry to get it back out again. In other words, it's precisely the properties of plutonium that make it attractive to build nuclear weapons out of that make it so hard to dispose of.
It's also very difficult to store because while an individual weapon may not be a critical mass, if you have tens or hundreds of weapons you have to worry about them getting close enough to worry about accidentally assembling a critical mass just from proximity, which, would of course, be bad.