I'm starting to think that writers of polemical doctrinaire atheism actually put in the errors on purpose. The goal is to produce a dynamic in conversation about the book that I'd call the Atheist Two-Step:
1. Someone points out that the particular religious belief disproven by the doctrinaire atheist is not really held by anyone as stated.
2. The doctrinaire atheist then says that religion is so obviously stupid and pernicious that one can't be held accountable for detailed knowledge of it.
This two-step, which really does occur and which I have had people do to me more than once, has indeed been a puzzling feature of the 'New Atheism' movement, at least to me. But I also wonder if the two-step is not so much intended to be directed against religion as it is against other atheists who hold that intelligent criticisms of religion do, indeed, require detailed knowledge of it. After all, the 'New Atheists' have no distinctive features as far as their critique of religion goes; it's difficult to find any feature of their approach that is not old and answered, and their approach is not very sophisticated -- the primary reason why other atheists keep criticizing them. What primarily distinguishes them as new is not that they've come up with a new or clever critical approach but that they go around loudly bashing atheists they think are too mild (namely, the atheists who are criticizing them for not being sufficiently sophisticated). So perhaps the two-step is less a response to religious critics and more a platform for mocking atheists who take religious topics seriously.
UPDATE: Miriam Burstein makes a good argument that this is a common polemical pattern, and neither particularly new or atheistic. The passage by Newman on the Prejudiced Man made for especially interesting reading.
UPDATE 2: In all fairness, as well, I was struck by this passage by Ophelia Benson (commenting on a claim by Smith that theists don't take atheism seriously enough to examine its arguments):
That would explain the way theists fail to engage with the arguments that atheists actually make, and it would explain the way they pretend atheists make silly futile claims that they don't actually make. That would be because theists aren't paying attention to what atheists say at all, they're just ignoring all of it and proceeding on their own pre-ordained track, like a runaway train ignoring all signals because the engineer has stepped outside for a sandwich.
It's noteworthy how easy it is to interchange 'theist' and 'atheist' here; indeed, I can even point to atheists who make much the same point with the two interchanged (i.e. atheists fail to engage with the arguments theists actually make), so you don't even have to take a theist's word for it. (To give just one example.) So perhaps, as well, what we are seeing is just a general feature of polemics (in whatever field) where emphasizing the wrongness of the opposing position becomes more important than knowing what that position is -- ultimately a self-defeating move, and, for that matter, poor polemical strategy, but one that the human mind apparently finds very tempting.
UPDATE 2: Ophelia Benson suggests a theist four-step; one which, I take it, is not a polemical tactic but a justificatory one, and certainly, where it is found, as dangerous as she suggests. [UPDATE 3: She clarifies here.]