The letter uses several denialist tactics, including,
1) Cherry-picked examples placed out of context,
2) Unsupported claims
3) Irrelevant distractions
4) Implications of conspiracy, and
5) Self-portrayal as stubborn heroes fighting against the odds.
The letter opens with the cherry-picked example of an APS member who resigned in protest of the word "incontrovertible" in the society's statement on climate change. From this single data point they somehow draw an unsupported trend line of a "large" and "growing" number of scientists who disbelieve climate change. Never mind the context, which is that the vast majority of scientists who actually study the climate agree that CO2 raises global temperatures. "Incontrovertible" is perhaps unfortunate verbiage – in science everything from gravity on down is subject to reinterpretation under new tests and new experiments – but the fact remains that an overwhelming majority of climate science supports global warming, and those who study it overwhelmingly agree.
Another unsupported claim is a "lack of global warming for well over 10 years now". This is likely based on the cherry-picked example that 1998 was particularly hot, ignoring the broader context. Stepping back and taking a look at the longer-term trend, warming is clear. They also claim that "computer models have greatly exaggerated how much warming additional CO2 can cause", but a look at the data shows that models have actually been fairly accurate, and certainly perform much better than the projections made by skeptics.
The letter then moves on to irrelevant distractions, such as the arguments that we exhale high amounts of CO2, and that many plants grow more quickly with CO2. These arguments are attractive to a layperson, but they completely miss the point of why CO2 matters. Ok, sure, plants grow better with CO2, but plants also prefer steady rainfall and they tend to dislike floods, droughts, and extreme heat.
Up to here we've seen the strategy used by this skeptical sixteen, but no legitimate scientific reason for doubt. What, then, is behind their denialism? The authors' real motives start to show through when they imply the conspiracy of an organized "multidecade international campaign" aimed at providing "a reason for government bureaucracies to grow" and "an excuse for governments to raise taxes," presumably on the fossil fuel industry that has funded about half of them. Ah, so the skeptical sixteen can't raise serious scientific quarrels with climate science – what they take issue with is the potential political response.
Here they may have a point: determining the appropriate political response is certainly less clear than climate change itself. It is therefore quite unfortunate that so many conservative minds like these are refusing to contribute their points of view to solving this problem, and are focusing instead on obstructionism and public confusion.
Beyond politics and funding ties, however, the authors' fifth tactic may reveal the most about their motivations: they see themselves as brave contrarians, and they take pride in standing up to the "international warming establishment" of the day, however accurate it may be. Consider their hyperbolic self-comparison to courageous Soviet biologists who were "sent to the gulag" for daring to accept the evil Western belief in genes.
In addition to the inherent appeal of being a David vs. Goliath style underdog, there is another good reason why scientists often take pride in being contrarian. Many of the most important scientific advances have overthrown widely accepted world-views, and met fierce resistance from the consensus of the day. Copernican heliocentrism, Einsteinian relativity, Darwinian evolution, quantum mechanics – all were heretical when first proposed, but now they are considered historical breakthroughs and their early proponents are scientific heros. Every scientist dreams of making such a paradigm-shifting discovery, especially in this era when so much of science is ultimately an incremental advance in a specialized sub-field.
Unfortunately, this group has allowed their political leanings and oppressed hero mentality to override their normally astute scientific instincts. Rather than making objective evaluations of the available data, they are beginning with what they want to find and searching for an excuse to support it, regardless of the evidence. Is anything in science "incontrovertible"? No. But when the overwhelming majority of data suggests danger ahead, we have a moral imperative to try and avoid it. Those who are skeptical of government intervention would make a much greater contribution to society if they would help shape the policy response to make it acceptable to all (or, at least, to most), rather than projecting that skepticism onto the underlying science.
Edit 2/2/12 to incorporate some points from discussion with Hank Campbell in the comments.
Like any human, scientists have inherent biases. Good scientists try to recognize their own biases, and constantly question their own conclusions from as many angles as possible. That's skepticism. When these sixteen allow their biases to predetermine their conclusions, that's denialism. And as Hank points out, neither liberals nor conservatives have a monopoly on denialism in the public discourse.
In the broader policy realm, it is a disservice to all when conservatives adopt climate denialism (a generalization, but largely true in Congress, at least). Climate change is not going away, no matter how deep we bury our heads in the sand. The longer we wait, the harder it will be to address. So why not find a mutually agreeable response now, if only to avoid a hasty one-sided approach later? The winds of politics are fickle, and there's no telling when liberals will regain a large majority. If climate is still unaddressed when that happens, we are likely to see largely partisan legislation emerge. When conservatives effectively take themselves out of the policy discussion, then the only people discussing policy are liberals. That's truly unfortunate, because the best solutions generally lie somewhere in the middle. Conservatives in the past have helped forge compromise policy that really worked and was satisfactory to everyone, such as the market-based cap and trade program that cut acid rain without damaging the economy.
So my message to conservate thinkers and politicians is this: America needs you in this fight. America needs your ideas and constructive criticism on policy options to address climate change. Please don't let denialists like the WSJ sixteen keep you on the sidelines.