Title says it all really? Any help would be much appreciated. I just need a few examples as I am struggling to find any...
Thucydides sometimes does not always make a proper distinction between facts and myths. Here is an example of him extending the Illiad into his historical work seamlessly.
Thucydides (460-395 BC) is one of the world's first historians. Although he uses methods we would not use today, he isn't lying or using "myth," per se. He is attempting to use history to be instructive. He is a political historian teaching lessons he felt would defend democracy by teaching his people moral lessons. Even around the time, the idea was criticized. If I recall, Aristotle (384 BC) delegated historical parallel to one of the lowest forms of political argument (although all forms of poetic arguments were altogether improper, illogical, so it is still above these). Consider for a moment how many times you have been told a dictator is like Hitler and thus something must be done or else we are all Chamberleins. While Thucydides might have meant well, the Greeks figured this problem out very quickly. Arguments about Helen of Troy were particularly common...did she start the war, etc...
Thucydides probably did understand that he was dramatizing his history by adding in dramatic speeches or Greek myth, since in the forward of his book he says that he will be attempting to provide a nonromantic view of history free from myth. He also selectively adds speeches and two person dialogue only in locations where it will be politically instructive.
This question is problematic because people during this time simply did not view history the same way that we do today. The Homeric tales, for instance, were treated as actual history, even the bits where Odysseus meets the sirens and the land of the lotus eaters. It's not that these events were viewed as "symbolically" true or something; people really and truly believed that these events actually happened.
This is not to characterize the ancients as stupid or feeble. They had the exact same brain capacity as we do nowadays. What they did not have was the benefit of hundreds of years of scientific experimentation and that process to inform them about the world. It is perfectly rational and reasonable to believe, for instance, that the world is controlled by the whims of spiteful gods when you do not have other evidence to refute that. Think of the issue of stellar parallax, for instance: the skies at night look an awful lot like an unchanging mass of stars that may differ in brightness but not in distance. It wasn't until the 19th century that we figured out how to measure that. Before that point, one can make the point that it was perfectly rational to look at that and say "because of this, I have to believe that the solar system is unique in this universe".
That being said, one of the things that separates Thucydides from so many other ancient historians is his lack of direct reliance on the mythology. He's clearly aware of the Odyssey, for instance, but by and large he seems to be of the belief that the gods are mostly if not fully within peoples' heads.
But that's getting a little off-topic, I think. What you are you asking, I think, is whether or not Thucydides ever wrote down something which we now know or at least strongly believe is factually incorrect? Sure. For one thing, The History of the Peloponnesian War is filled with speeches, speeches which, given the lack of recorded audio at the time, were almost certainly made up. Did the generals in question actually say something kind of like what he said they said to their troops? Maybe. He may have been there for some of them and may have relied on eyewitness accounts for others. The other issue, of course, with ancient history is that there was not a great deal of citing of one's sources.
The work does have the reputation, at least for an ancient text, for being relatively unbiased, however. That being said, the thing about writing narrative history is that there are always choices you make in terms of what to leave in and what to leave out. For a contemporary parallel the Band of Brothers series leaves out a great deal about the personal lives of the men of Easy Company, not to mention what happened during the vast majority of time they were in Europe. One could argue that that's outside the scope of the books... but isn't history everything, not just what fits into a narrative?