From Skeptical Science:
The greenhouse effect occurs because greenhouse gases let sunlight (shortwave radiation) pass through the atmosphere. The earth absorbs sunlight, warms then reradiates heat (infrared or longwave radiation). The outgoing longwave radiation is absorbed by greenhouse gases in the atmosphere. This heats the atmosphere which in turn re-radiates longwave radiation in all directions.
Some of it makes its way back to the surface of the earth. So with more carbon dioxide in the atmosphere, we expect to see less longwave radiation escaping to space at the wavelengths that carbon dioxide absorb. We also expect to see more infrared radiation returning back to Earth at these same wavelengths.
This is promptly shot down by Concerned Citizen/Matt Sykes at comments 6 and 8:
[Re] the picture showing solar light penetrating the atmosphere but terrestrial IR being trapped, what happens to the solar IR? The sun produces [more] IR at the frequency absorbed by CO2 [than] the earth. The atmosphere must therefore absorbs and re-radiate half of this back into space...
Point #3. Energy balance. So an increase in CO2 will absorb, and re-emit to space more IR from the sun as well as absorb and re-emit to earth more IR from the earth. Since the sun produces more IR than the earth how does the extra CO2 cause warming and not cooling? I am genuinely interested in the science behind GH gases, it is just that logically there seem to be problems with the theory.
That seems very plausible to me, and if true, this single observation would completely demolish the whole MMGW theory in one fell swoop.