I'm much closer to "below average" than to the "top" as far as LW users go, but I'll give it a shot anyway.

My point in posting this is simply to ask you—what, in your opinion, are the most legitimate criticisms of your own way of thinking ?

I assume that by "way of thinking" you mean "atheism", specifically (if not, what did you mean ?).

I don't know how you judge which criticisms are "legitimate", so I can't answer the question directly. Instead, I can say that the most persuasive arguments against atheism that I'd personally seen come in form of studies demonstrating the efficacy of prayer. If prayer does work consistently with the claims of some religion, this is a good indication that at least some claims made by the religion are true.

Note, though, that I said "most persuasive"; another way to put it would be "least unpersuasive". Unfortunately, all such studies that I know of have either found no correlation between prayer and the desired effect whatsoever; or were constructed so poorly that their results are meaningless. Still, at least they tried.

In general, it is more difficult to argue against atheism (of the weak kind) than against theism, since (weak) atheism is simply the null hypothesis. This means that theists must provide positive evidence for the existence of their god(s) in order to convince an atheist, and this is very difficult to do when one's god is undetectable, or works in mysterious ways, or is absent, etc., as most gods tend to be.