Things flying very fast through the atmosphere of the earth have the habit of insinuating in it. Would the kind of technology that you would need to do astroid mining really give you the ability to blow up a city?
Yes. You just need to nudge an existing sufficiently large asteroid onto a collision course. (Targeting a specific city is harder but I don't know how much harder.) There are how many near-earth and earth-crossing asteroids over 100m diameter?
A reality of physics, and one that doesn't get much play in science fiction, is that as soon as humanity gains space travel, anyone in the asteroid mining or space travel business will have city-busting capabilities at their fingertips.
It's there in classic sci-fi, but not so much recently.
This discussion was started in the comments to:
http://lesswrong.com/lw/gln/a_brief_history_of_ethically_concerned_scientists/
In the "Ethically Concerned Scientists" post, Izeinwinter commented:
A great start to a discussion here.
You've considered people going loons and some general security, but it would then become a hacker war along the lines of who could break the security and gain control of the space ships.
It doesn't address the problem of the leaders using the ships as threat weapons, since they have legitimate control, but can still make terrorist decisions.
And I'm terrified of your idea of turning spaceflight, which I see as the ultimate freedom, along the lines of Niven's Belters, into a state-controlled affair like the Soviet navy with political officers.
Now, one thing I think is a useful safety control that doesn't lead to worse problems is the destruct option. All major rockets have them right now, since if it goes out of control it's a huge hazard for a great distance. And although I don't like the idea of all personal spaceships being under a safety officers thumb, it might be better than the alternative of terrorist groups gaining control of asteroid mines and holding the world hostage.
You're right about great story potential though, in any of these scenarios.