Here's one I never thought I'd be writing about. The History Channel has presented a science documentary series called "The Universe". I watch it.... a lot. I'm a subscriber. I was a little surprised to find something questionable enough here to warrant a comment from me. Particularly when it wasn't just an off-hand comment, but a thoroughly thought-out segment. And particularly not when the idea was floated by Dr. Michio Kaku, one of the most successful popularizers of science since the late, lamented Carl Sagan.
The thing that perked my ears was the suggestion that Mars colonists would benefit from asteroid mining. The depiction here basically took the form of deflecting an iron asteroid out of its orbit so that it lands on Mars. Then, of course, the colonists would simply take the iron from it at their leisure.
It's not that the science here is bad. It's pretty sound reasoning as far as it goes. No, it's that the judgement is really, really questionable.
All other difficulties aside (such as coming up with the energy to accurately deflect a rock of that size moving at that prodigious speed), there's the obvious danger factor. An asteroid of the size discussed (about a kilometer across), would land with kinetic force rivaling the most powerful nuclear weapons. Surely you'd want your mine close enough to your colony to make the commute reasonable, but it's a fine needle you'd have to thread to not wipe out your colony with the delivery.
It's not like they need to do that. Mars is "The Red Planet" for a reason; that reason being that it's literally covered with rust. Iron oxide. On Earth we reduce that to iron by heating it with carbon. That doesn't exactly work on Mars, as elemental carbon is rare as unicorn farts, but it's still do-able in a couple of ways.
First, Mars does have water, at the poles. Electrolysis of the water would yield hydrogen gas and oxygen (and this makes it a ready source of oxygen for breathing). The hydrogen thus released could be used to smelt iron, as iron oxide combined with hydrogen yields elemental iron plus water (Fe2O3 + 3H2 -> 2Fe + 3H2O). So for the expenditure of some energy you get oxygen to breathe, iron to build with, and you even get your water back! With a bit of work, you might even be able to construct a roving foundry that spits out iron bars and breathable air from the sand it scoops up and recycled water. Fanciful, I know, but it's no more fanciful and it's a lot safer than pelting your colony with giant space bullets.
A second way is to use the carbon dioxide that composes the bulk of the Martian atmosphere. Throw some serious heat at it and it breaks up into carbon monoxide and oxygen. Once again we have oxygen to breathe, and in this case the carbon monoxide reacts with the iron to form elemental iron and more carbon dioxide (Fe2O3 + 3CO -> 2Fe + 3CO2). Since I don't much like carbon monoxide, and it's tricky to separate it from the oxygen so the latter can be used safely, I prefer what I think is the safer hydrogen reaction, above.
Be sure that either of these options is better than dropping an island on your head, so I'm really confused as to why this flight of fancy ever entered the conversation. Despite that bit of puzzling speculation, I still recommend the series and this episode. HERE IT IS.