Global warming has three basic claims: 1) the globe is warming, 2) it is warming in a pattern that doesn't match any cycles we've been able to reconstruct in the past, and 3) this abnormal fluctuation is caused by various heat-trapping factors, such as CO2 and methane CH4.
I cannot assess the scientific validity of these claims through my understanding of the research. Nevertheless, there are certain logical / argumentative issues in the denial of these claims that do not work. For instance
1) As evidence grows of warming, a claim is put forward that, yes, we are warming, but this is due to natural temperature cycles. Many of the same people will put forth another claim, which is that we have been cooling or steady for a decade. (More on this claim in a bit.) Such claims are possible if they occur at different time periods or in different places, but if they are supposed to be happening now, then they don't make any sense. It's a claim that the earth is both warming and cooling in the same place and at the same time. That's incoherent, and it is only entertained because each of the claims serves a rhetorical purpose at different places and times. Not all people who deny global warming make this mistake, but very many do, so you can be alert for it.
2) George Will, generally a very smart man, recently approvingly quoted social critic and columnist Mark Steyn, saying, "If you're 29, there has been no global warming for your entire adult life. If you're graduating high school, there has been no global warming since you entered first grade." That sounds really bad for global warming doesn't it, particularly if accurate? It does sound bad (well, for the argument; good for the world), but what does it really say? If I am 29 and I became an adult at 18, then that's 11 years. 2009 - 11 = 1998. OK, now if I'm a senior in high school, and there's been no warming since first grade, that's 12 - 1 = 11 again. Huh, 1998 again.
So removing the rhetorical devices, it's a claim there's been no warming since 1998.
But I wonder, what if I'm 30? Has there been warming since I became an adult? The answer is yes. What about if I'm 31? Yes. 32? Yes. How about the other way? What if I'm 28? Yes, warming since you became an adult. 27? Yes. What's going on here? How could there be warming for people of every age around 29, but not 29? The answer is that 1998 was a very anomalous year. Here's a graph of temps for the last century.
It may be hard to see on that graph, but 1998 is that black dot that jumps really far out from all the averages, and all the years around it. Every year in the entire 2000s has been hotter than every year on the entire chart except for 1998. Even the very last dot, 2006 which has a slight dip (yay!) is hotter than 1995, 1996, 1997, 1999, and 2000.
The obvious point is "don't fall for the 1998 gimmick". The bigger point is "be wary of any argument that hinges on selecting just the right example.
3) Beware of a set of arguments where mistakes are never corrected when they are pointed out. For instance, there is a myth floating around that in the 1970s, all the scientists thought there was an ice age on the way. Clearly they didn't know what they were talking about then, so they must not know now. First, there's an obvious problem, which is assuming that scientific knowledge never improves. If someone said, "In the 20s, they didn't know how to land a man on the moon, so they must not know now," you'd laugh at them. Science has changed a lot since the 20s and in fact we landed someone on the moon already. Now, from the outside we don't know if climate science has gotten better or not (it has), but that's just our ignorance from not knowing the field. It's entirely possible that mistakes that were made 20, 30, 40 years ago would not be made now, because we know more.
All that aside, the real point here is that this "scientists all thought the ice age" was coming is just a myth. There never was a consensus at that time. This fact has been pointed out by the American Meteorological Society. Here's one of the most relevant quotes:
... despite active efforts to answer these questions, the following pervasive myth arose: there was a consensus among climate scientists of the 1970s that either global cooling or a full-fledged ice age was imminent ... A review of the climate science literature from 1965 to 1979 shows this myth to be false. The myth's basis lies in a selective misreading of the texts both by some members of the media at the time and by some observers today. In fact, emphasis on greenhouse warming dominated the scientific literature even then.
There have been other analyses of the myth as well. What's important is that even when the myth is proven to be false, it continues on. No retractions, nothing. You just keep reporting the myth. This is how political arguments work, repeating the talking point to get traction, not scientific ones. The fact that evidence doesn't change arguments is an indication that one side is really presenting a political argument.
4) Beware the great conspiracy of peer review.
Most denialist literature exists on web sites, in white papers from think tanks, books from non-academic publishers, and other non-peer-reviewed formats. Not all, but it's certainly dominant. Moreover, you can't find any large scientific bodies who are skeptical of climate change. Why is that? Either peer reviewers are rejecting such papers for valid reasons or... they are rejecting them because they control what does and does not get published and they will never allow a competing view to appear. In other words, it's a conspiracy, covering journals and scientific bodies around the world.
Now, am I saying that peer reviewers never have their unjustified biases? Certainly not. It's not uncommon for a reviewer to have a biased view for whatever reason, usually to protect their own reputation. Sometimes these biases can spread to large number of reviewers. This happened in my field of linguistics in the late 60s to early 80s, when Chomskyan linguistics dominated everything. If you didn't work within those assumptions, it could be tough to get in the top journals. What did the field look like then? The so-called top journals were dominated by Chomskyan linguistics, and many of the top departments were as well. Yet at the same time, there were other smaller journals publishing fine stuff. There were other departments who had non-Chomskyan interests. There were members of departments who disagreed with Chomsky, but were still around and getting tenure. Non-Chomskyans had their conferences and all. Chomskyans thought they were wrong, but alternate research programs continued on.
This isn't what the state of climate research looks like. There are only a small number of researchers out there skeptical of global warming who can actually write something good enough to pass peer review, and, oddly for a conspiracy, they do get published sporadically. The number is small, and refutations are often published soon thereafter. In other words, the picture is neither one of a global conspiracy where everything that doesn't tow the party line gets banned nor one of a bias among mainline researchers. The picture is instead that the majority of climate research supports global warming and only a few skeptics write decent enough stuff for acceptance.
5) Beware the great conspiracies in general. There are a million claims about great conspiracies among "lay" skeptics, i.e., your average conservative Joe. This is a conspiracy by liberals who want to destroy the economy. It's a conspiracy by liberals who want to seize power. It's a conspiracy of funding. Cap and trade is a hoax for Al Gore to make a 100 million dollars (often the same round number is repeated). In many minds, Al Gore seems to be a great puppet master making the world dance for him. You think I'm kidding? Read the 200 plus comments that were posted on Yahoo after an astronaut dared to mention shrinking ice caps.
People in general are quite incompetent. A conspiracy involving more than six people wouldn't make it a week.
6) Organizations which are trustworthy when you cite them are not trustworthy when they disagree with you. It is very common to quote a scientific source in a skeptical argument as much as possible, since it lends credibility to your point of view. But what happens when that source you quoted disagrees? They suddenly become part of the conspiracy or are brainwashed.
7) Smart people don't know everything because they are smart. It's always really tempting in an argument to quote someone who's really smart who agrees with you. For instance, Steven Hawking believes that man-made climate change is possibly the greatest issue facing humankind today. Dang, it's Steven Hawking! I mean, it's Steven Hawking! So clearly that means something. Well, maybe, but it's hard to know. Has he ever really researched climate science? No real idea. Similarly skeptics can pull out a name periodically. There's a guy who got the Nobel on Physics in the 70s who made some skeptical remarks at a conference once. But, as far as anyone can tell, he's never done any actual research on climate science ever. No articles of any sort. I don't doubt the man's smart, but that doesn't mean he's educated on this topic. Larger point: Just quoting someone cool doesn't add much weight to anything. You need to know if they've ever actually done research on this.