Let’s stipulate that carbon exhaust generates a negative externality in the form of climate change.  Further stipulate that this externality is large enough to justify limiting carbon exhaust through a carbon tax and/or cap & trade.

Given those presumptions, how would you implement?  Here are some of the challenges.

1. How to estimate the value of carbon emissions.  Cap and trade is supposed to deal with this through market pricing.  But that presumes markets have enough information to set a rational price.  Markets set prices through individual agents making specific cost/benefit calculations. The benefit of carbon reduction appears very large — but how large, specifically?  The specific benefit of carbon reduction, measured in dollars per kg, is not only unknown, but unknowable.  This remains true even when we all agree the number is large.  Markets cannot solve this problem.
2. Prisoner’s dilemma.  All countries are better off if they all follow the rules.  But each individual country has an incentive to cheat, because carbon-dirty energy (coal) is, for now, cheaper than clean energy.
3. Collusion.  Carbon buyers and sellers each have an incentive to form cartels.
4. No global enforcement mechanism.  What do you do if a country simply ignores its carbon obligation, or does something like #2 or #3 above?  Since 1945, the United States has been the backstop for global multilateral agreements, backed up by force if necessary, whether in the form of trade, financial or military intervention.  As US GDP as a % of world GDP declines, and as the US population becomes less willing to intervene, this situation cannot persist indefinitely.  There is nothing to replace it.
5. Incentive to cheat varies by country, due to differences by country in energy intensity, energy cost, energy mix and so on.  Markets are supposed to take care of this problem through cap & trade, but this leads back to the problem in #1 above.
6. Costs are borne unevenly within countries.  In the most extreme case, a despot in a poor country might sell all his carbon credits and keep all the proceeds, reclining in his solar-powered palace as his subjects shiver in unheated hovels outside.  Actual countries won’t approach this extreme, but it’s easy to see that the greater the concentration of power, the more the benefits of cap & trade will go to leadership, while the costs are borne by the masses.  Therefore, cap & trade probably increases income inequality in non-democratic countries.

Note what this essay does NOT say.  It does NOT say that carbon limitations are a bad idea.  It does NOT deny climate change due to carbon emissions.  It solely concerns implementation challenges, which appear huge.