I think stuff like this is pretty amazing. It appears using the ocean to suck up CO2 is the way we (science) wants to go to solve this problem.
I read in Popular Science that they also considered doing this with finely ground up iron. The iron is supposed to cause huge blooms in phytoplankton which suck up lots of CO2. The food chain goes into effect, they get eaten, things die and the CO2 winds up sinking to the bottom of the ocean. This was even posed as being a great thing for the ocean as abundant food supply would cause a huge boom in ocean population in general.
Apparently there was a ship that had tons of iron powder on it that was going to go ahead and just spread it out into the ocean, but they were blockaded and otherwise discouraged because no one could tell what the long term effects were going to be.
Things like this are tricky. I get scared when we talk about doing things to our oceans that are going to affect our entire planet. Can we really judge what the long term effects are? Sure we might get rid of half the CO2 in our atmosphere, but what are the ramifications to our ocean environment? Are we going to kill off half the Coral Reefs in the process? I just think it's hard to judge what the widespread and maybe unseen ramifications are.
Very cool stuff, but scary when you start to think of doing things that would show large scale results in a small amount of time. Changing our entire atmosphere/ecosystem in the course of a year or two (in the powdered iron example) makes me worry. I'm reminded of The Matrix when Morpheus says we scorched the sky to try and stop the machines, but it didn't work.

Now we're stuck with a shitty sky and still have killer machines running around!