Let me start by saying your question is one of what Prof. John Lee calls "the big 5 questions" of Greek history. It's been a question for 2,400 years and there's no consensus that's ever popped up as far as I know.

That is not least because Thucydides was inventing the field of "scientific" (to borrow a word I don't care for) history from whole wool. He did not have a lot of the analytical tools we use as second nature now. He was working it out on his own.

I also want to point out that questions like "how much can we trust" a historian, or how biased they are, are methodologically flawed. Trying to produce history wie es eigentlich gewesen ist is a 19th century model of writing history, nevermind reading it. It's much more helpful to read a text on its own terms and ask why the author would write in such a way - which is a question you've started asking by wondering about any anti-Athenian leanings Thucydides might have had. That is not to say history is devoid of truth, but rather that truth is subjective for both the writer and the reader. To borrow a phrase from one of my favorite academics, "If it's truth you're interested in, Dr. Tyree's Philosophy class is right down the hall."

Ok, caveats out of the way. What can we tell about Thucydides? There aren't a lot of data points I'm aware of that we can check. Maybe the most interesting one is Thucydides' report on the Peisistratids. He gives two versions of the story: one the story the Athenians tell, and the other the "true" account. The traditional "Athenian" version is that when Pisistratus died of old age, Hipparchos seized the tyranny, and was later assassinated by Harmodios and Aristogeiton, liberating the state and establishing democracy. In fact, Th. says, it was Hippias who became tyrant, and Hipparchos was assassinated not for political reasons but for his attempt to seduce Harmodios (well, sex is always political, but we're not talking about pro-democracy guerillas here). It was the Spartans that eventually stepped in and ended the tyranny.

Th. says he knows his story is correct because he has physical evidence - specifically an altar dedicated by the son of Hippias. As it happens, that altar still exists. To the extent that this altar is evidence of anything, it seems as though Th. faithfully reproduces the information it provided him. Th. later references the tomb of Archedice, the daughter of Hippias also as evidence for his story. To the best of my knowledge, that tomb no longer exists, but given Th.'s treatment of the altar, I don't know why he wouldn't be reporting the details about the tomb accurately.

I can't think of other archeological corroboration of Th.'s narrative (paging /u/Iphikrates), but at least this one episode illustrates his method. Speaking of which, Th. happens to discuss some of that himself. He says he began writing as soon as the war broke out, but I think the consensus is the earlier books are heavily revised, while of course the last one ends mid-sentence. I'm not going to discuss his Archaeology here, and skip right to section 22 where he discusses his methods.

Insofar as these facts involve what the various participants said both before and during the actual conflict, recalling the exact words was difficult for me regarding speeches I heard myself and for my informants about speeches made elsewhere; in the way I thought each would have said what was especially required in the given situation, I have stated accordingly, with the closest possible fidelity on my part to the overall sense of what was actually said.

Ok, so we know he's relying on his own memory, and on the memory of others. First, it's important to know he's upfront about this and acknowledges the limitation this imposes on him. Second, and this is too often overlooked, he insists on remaining as close to the source as possible. This is very different from Herodotus, who will say "The Greeks say this, the Persians, that, and the Egyptians, the other thing. You figure it out."

Th. also distinguishes his speeches from the events of the war:

About the actions of the war, however, I considered it my responsibility to write neither as I learned from the chance informant nor according to my own opinions, but after examining what I witnessed myself and what I learned from others, with the utmost possible accuracy in each case. Finding out the facts involved great effort, because eye-witnesses did not report the same specific events in the same way, but according to individual partisanship or ability to remember.

Ok, Th. tells us he's doing multiple interviews and checking his information against his own memory (and you need to remember he was a general in that war - probably made him as informed as one could be). Now, Th. doesn't usually cite his sources, so we have no way of evaluating how well he reproduces them or uses their information, but we do know he's thinking about the problems of memory. We also know he will check his oral sources with archaeology like that altar when possible, and he will call bullshit on stories he hears that don't hold up to fact-checking.

Can we know he practiced his method consistently? No. Can we know he thought about method and identified problems with his method? Absolutely. Can we trust his speeches? He's upfront with us that memory is a poor source for history, and he claims to do the best he can.

I am not sure what more you would want from a historian.