Is the problem the cap or the trade?
Environmentalists are often uncomfortable with the "trade" part of cap and trade, preferring a more traditional non-market regulatory scheme ("just cap"). There are two common families of environmentalist counterarguments to cap and trade. One is that the market is inherently degrading, that it's immoral to use dirty* money to take care of something important like environmental protection. Little justification is ever given for this way of thinking, and as a pragmatist (in the lay and philosophical senses) I don't see much merit to this sort of blanket moralism.
Another line of attack on the trade part of cap and trade has to do with the fact that the people causing the problems in the first place are the big fans of trading -- business and industry. So there seems to be reason to suspect that making a concession to them by building on a market mechanism would weaken an environmental policy. My pragmatism would again move me to reject any simplistic blanket declaration that "businesses like markets, businesses destroyed the environment, therefore markets are bad." But it's more than plausible that the market mechanism could introduce distortions and unintended consequences that undermine the environmentally protective aims of a cap and trade policy.
This article by Janet Wilson seems like it's going to lay out some of those sorts of distortions and unintended consequences by taking a skeptical look at some existing cap and trade schemes. While she shows that, contrary to some pro-cap-and-trade hagiographies, these schemes haven't achieved their goals, she doesn't show that it was the "trade" part that was the problem. In every case, it seems like the problem lies with the cap. That means that eliminating the trade and going to a pure cap wouldn't fix things.
Wilson starts off with the U.S. Clean Air Act's anti-acid rain cap and trade. Her conclusion is that it helped, but hasn't done enough. The culprit, it becomes clear, is the cap -- the science at the time the policy was made was too optimistic about how much emissions needed to be reduced to de-acidify the northeast's rain, so the cap was set too high. But this means that a purely regulatory approach, which would have been based on that same optimistic science, would have made the same mistake and also set too high of a cap.
Next, Wilson discusses a cap and trade plan to reduce smog in Los Angeles. Again, it made some progress, but didn't fix the problem. At first glance, problem #1 with the policy seems promising as a counterargument to cap and trade. Due to political pressure surrounding past recessions and the California energy crisis, pollution credits were over-allocated and compliance was poorly enforced. It's a classic case of regulatory capture by big business. However, big business did its dirty work not by fancy trade maneuvers, but by getting the cap loosened. Had LA had a pure cap, polluters could have pursued the same strategy and convinced the government to loosen or not enforce the cap. Problem #2 in this case also doesn't tell us much about the desirability of cap and trade. Much of LA's pollution comes from cars and trucks, which the state and local authorities who created this system aren't allowed to regulate through any policy mechanism.
Wilson moves on to Europe's cap and trade scheme for greenhouse gases. She points out that it has made little impact, because emissions credits were over-allocated and offsets weren't verified. Just as in the LA case, though, these are problems with setting the cap, not with trading the permits. A purely regulatory approach could just as easily have been too generous in the emissions it allowed polluters to get away with. Finally, Wilson documents the same problem afflicting the new cap and trade plan implemented by 10 northeastern states.
In passing, Wilson twice mentions something that could be a serious criticism of cap and trade plans: the "environmental justice" argument, which holds that cap and trade would allow uneven distribution of pollution (a few polluters could continue being really dirty as long as they can get credits from somewhere else that's super-clean). In addition to the straight-up distributional inequality, you could get added problems if, as is likely, the dirty polluters were the ones in poor neighborhoods and/or neighborhoods of color. The catch with this argument, though, is that it depends on the nature of the pollutant and the size of the trading area. If the dispersal of the pollutant's main effects is over a smaller area than the area in which it's traded, you can get unfair concentrations. But if the pollutant disperses more widely than the trading area, it's irrelevant where it's initially emitted. Greenhouse gases have global effects, so they fall in the latter category -- one state or country can't create a bubble of non-changed climate around itself by eliminating carbon emissions, because that reduction will be spread out to the whole world.
Note as well that another popular mechanism for controlling greenhouse gases -- a carbon tax -- could suffer from the sorts of problems Wilson outlines just as well. Setting the tax rate for a carbon tax requires estimating a cap based on the environmentally-needed emissions reduction level (plus whatever extraneous political considerations enter in), as well as monitoring and enforcement by the government. Bad science and business pressure could easily result in a too-low tax, and poor efforts in catching violators.
*There's an interesting point to be made here from a Mary Douglas-ian perspective about the foundational metaphor of money and markets as dirty and how that shapes thinking about environmental issues.