Having followed these threads, and being a (weak) atheist (i.e. agnostic in common parlance) myself, I would say that criticism of theism and Christianity on this board as often draws on well-reasoned logic (i.e. appealing to induction, Ockham's Razor, etc.) as it does on fallacies. The most common fallacies I see here are caricaturization of belief through "straw-men" arguments and the use of misinformation in one's argumentation. These faults really have nothing to do with "atheism" as they do with polemics and styles of rhetorical argument. On this board, discussions of religion typically are polemically charged and rather than carefully laying out ones' reasoning and the many complexities of the subject (as Carl attempts to do here), it is usually much easier to take short-cuts and attack simplified caracitures or present common sensical or unresearched claims that may not have any evidentiary value. That's just the nature of freewheeling debate, especially in forums like these. And it happens even with the most intelligent, rational, and otherwise very careful writers. Even those wanting to present a matter positively or as objectively as possible may fall victim to the vice of oversimplification or distortion...our own processes of cognition (with its classification and reification schemes) militate against this. As Narkissos ably pointed out in the previous thread, Dawkins' characterization of Christianity is a narrative of his own construction that misrecognizes its subject as much as it describes it, and the emphasis in that thread on objective basis of belief (e.g. on a written text that is "beheld" contra Hebrews 11:1) is certainly an opportunity for believers to affirm their subjective experiential basis of faith. And too often, I see people here posting Internet misinformation about religious topics, such as the "Horus/Krishna/etc. was born on December 25th/in a cave/baptized/crucified/raised three days later just like Jesus" canard that is just plain wrong.
I want to be clear too that in such online discussions, fallacies are just as often made on the other "side", such as treating an inductive conclusion as equivalent to faith, misplacing the burden of proof, and developing "straw-man" arguments and misinformation on matters that are being attacked on polemic grounds (such as evolution, for those who do not accept a theistic view of evolution). Unfortunately, online discussion boards are not the place for rigorous, careful debates. However, the caliber of discussion here is far superior than what is found elsewhere on the net, such as ... oh, say, Youtube comments. I also wish that "anti-theism" existed as a ratified word, as it seems better suited to describe the more polemic stance as opposed to the neutral a-theism (which, if taken etymologically, would imply a "without theistic belief", which best describes my own personal belief system).
Also, I want to give a belated welcome to Carl who has written some imho very thoughtful and polite comments on these various subjects.