In the example of the rolling Hiroshimas, may I add that these cars are well over two hundred years old and have been rusting and going without maintenance since a great big nuclear war? There's no indication cars randomly blew up when new, it's probably because of how old and poorly maintained they are.
Wouldn't the nuclear isotope disappear then? However I do lack knowledge of nuclear physics so perhaps not.
Depends on what it's using. Plutonium, uranium, radium, handwavium, etc.
Ah, handwavium. Of course.
Well, they don't exactly elaborate what was the fissionable material of choice by 2077.
The general rule is that the more radioactive it is the faster it disappears. The fresh material in a nuclear fission reactor gets burnt up quite quickly, so they have to be refueled every now and then (that's not due to the natural radioactivity, though; the reactor is critical during operation, that's how it produces net energy). Nuclear bombs also have to be maintained because of that, although they'd last longer because they're subcritical when they're not exploding (with a very long half-life, too).
No matter the material, nuclear bombs have to undergo maintenance, though, as they're quite complicated devices. I'm not sure what lifetime modern (as in, the latest bombs from around 1992) bombs were designed with, but apparently most older american bombs were designed with a shelf life of about 20 years. After that their reliability goes down due to degradation of explosives and corrosion of the cores and so on.