People know best what they've studied the most is my rule of thumb. That's why I go to a medical doctor when I'm sick, but take the dogs to a veterinarian when they're sick. I call up a plumber when the water heater needs replacing, and take my car to an auto mechanic when it needs work. And not vice versa on any of them. It might be true that the auto mechanic is also a good plumber. But, odds are, the person who focused on learning plumbing is the better plumber.
None of this should be a surprise to anybody, yet it seems in practice that it is once we come to climate. Let's be a little more specific in that -- make it the question of whether and how much human activity is affecting climate. There are many other climate questions, but it's this one that attracts the attention, and lists of people on declarations and petitions. If you look only at the people who have professionally studied the matter and contributed to our knowledge of the matter, then the answer to the question is an overwhelming 'yes', and a less overwhelming but substantial 'about half the warming of the last 50 years'.
I've tried to set up a graphic (you folks who have actual skills in graphics are invited to submit improved versions!) of 'the way to bet'. The idea is to provide a loose relative guide as to which fields most commonly have people who you can have the greatest expectations that they have studied material relevant to the question of global warming and human contributions to it from a standpoint of the natural science of the climate system.
Climatology, naturally, is on the top tier -- many people in that field will have relevant background. Not all, remember. Some climatologists look no further than their own forest (microclimatology of forests -- how the conditions in the forest differ locally from the larger scale averages) or other small area, or small time scale. Still, many will be relevant.
Second tier, fewer of the people will be climate-relevant, but still many. Oceanography, meteorology, glaciology.
Third tier, most people will not be climate-relevant. But some have made their way, at least, from those fields over to studying climate. That includes areas like Geomorphology (study of the shape of the surface of the earth) and quantum physics (the ones who come to climate were studying absorption of radiation).
Fourth tier, almost nobody is studying things relevant to the question I posed. The extremely rare exception does exist -- Judith Lean has come from astrophysics and done some good work (with David Rind, a more classically obvious climate scientist) regarding solar influence on climate. Milankovitch was an astronomer/mathematical analyst who developed an important theory of the ice ages.
Fifth tier, I don't think anybody has studied the question I posed directly. I do know a couple of nuclear physicists who have moved to climate-relevant studies. But they essentially started their careers over with some years of study to make the migration. In this, it's more a matter that they once were nuclear physicists. After some years of retraining, they finally were able to make contributions to weather and climate. At which point, really, they were meteorologists who happened to know surprisingly large amounts about nuclear physics.
Sixth tier, I wouldn't include at all except that they show up sometimes on the lists. My doctor is a good guy, bright, interested, and so on. But it takes a lot of work studying things other than climate to become a doctor, and more work after the degree is awarded to stay knowledgeable in that field. That doesn't leave a lot of time to become expert in some other highly unrelated field.
[Figure removed 14 September 2009 -- See Intro to Peer Review for details]
Suggestions of areas to add, or to move up or down, are welcome. I'm sure I have missed many fields and others are probably too high or low.
For now, though, if you're not an expert on climate yourself, I'll suggest that if the source is in the first two tiers, there's a fair chance that they've got some relevant background. If they're in the bottom 3, almost certainly not -- skip these. And the third level, is probably to skip but maybe pencil them in for later study, after you've developed more knowledge yourself from studying sources on the first two levels.
This ranking, of course, applies to the particular question asked. If the question is different, say "What are the medical effects of a warmer climate?", the pyramid would be quite different and MD's would be the top tier. Meteorology would move down one or two levels. Expertise exists only within some area. As I said, nobody knows everything.
Update:
frequent commenter jg has contributed the following graphic:

A general good change he's made is to split between general skills, that can transfer to studying climate, as well as what particular sorts of detailed skills or knowledge one might have. Almost everyone, for instance, involved in studying climate knows some statistics and mathematical analysis. Many fields also require such knowledge, so those would find it easier to move over to climate.
Different good change he made was to put the question directly into the graphic. This is important. As I said, but didn't illustrate, the priority list depends on exactly what question is at hand.