I suppose I should show the math, so someone could correct me if it's off. This source [1] puts the number of Joules in a gallon of gas at 130,000,000. Let's take a slow gas pump and assume five gallons in a minute. That's 4.3 megawatts [2]. For one car at a time. You can fiddle with that number if you're willing to be brutal on how far the electric car can travel or if you think people will stop every 50 miles for a 30 minute electricity topup, but no matter how you slice it you're going to need a major electrical network upgrade. I think this is a good idea anyhow, but in a country that would rather buy bread and circuses than bridges I'm not sure how it's going to happen.
[1]: http://www.evworld.com/library/energy_numbers.pdf
[2]: http://www.google.com/search?q=(1.3*10**8)+joules+per+30+sec...
People already steal copper wires and screw up our infrastructure that way. I honestly can't imagine a world in which greedy idiots don't screw everyone over given how expensive those batteries are and that makes me sad.
Such systems must already allow you to keep the battery as long as you want and to use it as often as you want (for as long as you have a contract), they must allow you to charge yourself, otherwise they wouldn't make all that much sense. The idea is that you don't have to change batteries for daily commutes or short trips (you charge at night), only for longer trips. (This is something that works much better in densely populated countries with little sprawl — the US might not be a very good candidate. I think Israel is trying out such a system in some way, its smallness makes it ideal.)
It's like a flat rate, some drive little, some drive more, but just because the battery is rented doesn't mean that driving behavior will change all that much. There is only so much you can drive and charge.
I also think that it would be somewhat involved to sell the battery on the black market. You have to at least get a replacement battery before your contract is up, so where's the advantage in selling your old battery on the black market? You might be able to profit a little, but you would also need scale, you need know how (how to manipulate the data those batteries would no doubt be collecting) and you need to be able to hide from the police. Nothing unheard of, but also no show-stopper. (People already do this with odometers and hardly anyone cares.)