Alarmist maybe, but I wouldn't call them completely unfounded. Material from spent fuel or decommissioned reactor cores is a bit more hardcore than your average radioactive material that you might find lying around somewhere. The stuff has to sit in ponds for several months after they are taken out to let some of the more active stuff fizzle out before you can even begin to deal with it. Some countries bury the spent fuel but if it is reprocessed, the waste generated is even more radioactive still - this is so dangerous it simply has to be stored in a very safe place indefinitely.
This is a bit mixed up. Waste doesn't need to be stored indefinitely because it is more radioactive. That doesn't even make sense. The more radioactive something is, the
faster it becomes safe. The stuff that needs storing for a long time is actually not particularly active, which is precisely why it needs storing for so long - it will still be not particularly active in a thousand years, when more active material will have long since decayed.
But that's all pretty much beside the point, because no matter how radioactive the waste is, you can't make a nuclear weapon out of it.
Commercial reactors are perfectly capable of producing weapons-grade plutonium if the fuel is taken out at the right time. The only difference is that it is more commercially viable to leave them in longer when it is being used for electricity generation. Although granted, you'd still need the right facilities to reprocess the spent fuel.
Firstly, most commercial reactors are thermal, not fast, reactors, so they're a long way from producing significant amounts of plutonium. Secondly, so what? If you're already capable of playing around with reactors to get plutonium and reprocessing it to get weapons grade, you can do so already. Putting a few reactors in cars won't make any difference here.
Also, a fact not widely advertised is that the reactors used in nuclear submarines actually use a very highly enriched uranium as their fuel, sometimes as much as 90% fissile, which is enough to make bombs with.
Again, so what? What does that have to do with nuclear powered cars? I completely agree that making weapons grade fissle material freely available to the general public would be a fairly silly idea, but that's not what anyone has suggested. At least I certainly hope they haven't.
Regarding getting hold of radioactive materials, I'm not sure how the laws work wherever you are, but the ones in the UK are highly restrictive regarding anything radioactive in terms of accountability and the like. We use some embarrassingly weak sources at work (<10 mCu beta) and they still have to all be signed in and out and kept in a safe when not being used and stuff. If any go missing, we get prosecuted. And of course, that's just the laws regarding the non-fissile material. You should see the legislation governing fissile material...
The laws governing radioactive materials in the UK are so strict that until a few years ago it was dumped straight out of hospitals and onto bathing beaches. There's plenty of accountability, but very little security. Heck, if you really want to make a dirty bomb you can just order a bunch of smoke alarms. Nuclear cars might mean more radioactive stuff around, but it's really not that hard for someone to get hold of plenty right now anyway.