Per Myhrvold's idea (Fareed Zakaria, CNN) for solving global warming, adding a certain volume of sulfur dioxide mist at a certain rate to the outer atmosphere will help to reflect sunlight by 1 degree, which will "check" the amount of carbon dioxide which is responsible for what is believed to be global warming. My question is what would be the chemical fallout of such an endeavor, and will it cause more harm to the planet than it will do good?

Sulfur dioxide in the atmosphere will absorb water to form sulfurous acid. The sulfur dioxide can be oxidized at higher atmospheric levels to sulfur trioxide, SO3. That will absorb water to form sulfuric acid. Both of those acids would contribute to "acid rain" which kills plants, corrodes anything metal, etc.