Reading this article [treehugger.com] about a large area of debris in the Pacific Ocean made me think immediately of space debris. It's not the action of how things get there -- on one hand you have junk being dropped off ships, on the other you have junk dropped off rockets or satellite -- but the question of how to remove it.
Or maybe the question is: is it feasible to remove it? The article about the ocean debris claims that the area is approximately twice the area of the continental United States (~16 million km2 [Wikipedia]). The surface area of a sphere with a radius of 6600 km, i.e., less than 250 km above the Earth's surface or near the lower bound of Low Earth Orbit, is approximately 500 million km2.
That's a lot of area in either case. I don't think you just send the CCC out to the problem areas in rowboats or spacesuits to pick up the junk. What you would need is something automated. But even then: what do you do with the junk after you pick it up? How do you measure what you're doing so that you know you're doing something good, and not causing a new problem? (Recovering 1000 kg of space debris seems like a nice thing to do... unless you end up just dropping it into someone's dining room in Perth.)
It's a problem -- and I consider the irresponsible dumping of garbage a problem, even if it is out of sight -- that occurs on a huge scale that's difficult to understand. Because it occurs in a remote location, there is no real urgency to remove the junk; if the cost of large-scale cleanup is X, the amount of money lost due to leaving the junk in place (decreased fish harvest? re-routing ships?) is Y, and X >> Y, I don't see any governments or other institutions making that investment. What if it was possible to use this as a test bed for remotely operated cleanup? It would be a smaller-scale endeavor, thus taking longer, but it would be win-win: amount of loose garbage decreased plus field experience for the pickup system. Is there any market for the junk that is picked up? Is there any market for such a remote system?