- It's a waste of time.
- It gives pseudoscience undeserved credibility by putting it on an equal footing with science.
- There are few people in the audience who haven't already made up their minds.
- Most of the people in the audience can't distinguish good from bad arguments.
While Dunning correctly points out some major flaws in how formal debates have frequently gone, and I agree that such debates should be discouraged, I think there are cases where they are worthwhile--it depends on the formulation of the resolution to be debated, the setting of the debate, and, perhaps most importantly, the quality of the debater. Too many creation/evolution debates have involved scientists who believe themselves to be good debaters, but who don't understand how debate works and aren't sufficiently familiar with creationist arguments to an appropriate breadth and depth. Unfortunately, many of those scientists think they won the debate or did a passable job when in fact they performed very poorly.
The resolution to be debated should be formulated so that there is a clear burden of evidence on the promoter of the pseudoscience, where it belongs. It's a mistake to formulate a debate resolution as a false dilemma, where if the scientist can't refute scattershot attacks, the pseudoscientist wins. Duane Gish of the Institute for Creation Research won most of his debates by not only engaging in such a shotgun approach (the "Gish Gallop"), but also by refusing to talk about the age of the earth or flood geology, thus freeing himself from having to present any positive evidence in favor of his view. (I spoke a bit more about Gish's debate success and how to successfully counter his debate strategies in my workshop session at this year's American Humanist Association conference.)
The setting of the debate is also important, and is relevant to Dunning's concern about audience. An academic debate at a university is more likely to have audience members who are actually interested in the evidence than, say, a debate at a church. It's also significant whether the debate is being recorded and will be distributed further--a well-done debate that is recorded and transcribed, and distributed in the form of a book, DVD, or online is going to have a much larger audience and may have much more significant consequences than the potential persuasion of five people in Dunning's example. There are also debates conducted in written form, which provide the possibility of much more comprehensive argument and references to other material than an oral debate on a stage or on television, which I think generally makes them preferable.
The concern about giving a pseudoscience proponent undeserved credibility is a real one, and for that reason it's probably a good idea for the debater to be someone of similar or lesser public stature, as well as someone well-versed in both debate and the details of the pseudoscience's claims. Proponents of pseudoscience often issue challenges to prominent individuals for the primary purpose of getting publicity from it, which they may get to some degree either from denial or acceptance--but much more from acceptance if they so much as appear to hold their own.
Dunning dismisses the concern that failure to debate leaves pseudoscience unchallenged, but I think there is a real potential concern here, as a refusal to debate can give proponents of pseudoscience a rhetorical weapon when there's the appearance that no one is willing to challenge their arguments. This can, to a large extent, be defused if you can point to resources that refute the proponent's claims in detail, and make the counter-argument that the proponents views aren't deserving of a public forum. But in cases where the proponent's views have received a large public following and there aren't comprehensive resources that refute them, or such resources are little-known, I think that builds a case for debate.
I think Dunning is right that it's generally better to produce direct responses to pseudoscientific claims in a one-way format, but even that can be a form of debate to the extent it actually engages the proponents and they respond. What's distinctive about a debate--at least a good one--is that it does involve engagement by both sides with the arguments and evidence of the other, and produces a record of that engagement for others to examine. That has advantages over siloed separate arguments that never directly respond to each other. I think that such engagement should be beneficial for scientists by identifying forms of misunderstanding that need corrections in the form of better communication, as well as locating possible weaknesses in their own evidence and arguments that need further work. It's also beneficial for the proponent of pseudoscience in that it puts them into a situation where they must, at least momentarily, think about the arguments and evidence against their positions.