I'm not that familiar with Egypt, but I know John Lee's (professor, Santa Barbara) 5 top problems with Greek history.

1. The Homeric Question: Were the Iliad and Odyssey composed by one person, two people (possibly the Odyssey by a woman), or many over the course of centuries? I think ML West's interpretation that they are the product of hundreds of years of oral tradition (a theory that goes back to Parry and Lord in the early 20th century) remains, if contested, the majority opinion.

Related, 2) Was the Trojan War a historical war? Lee's opinion is (and I got this from conversation; sorry I can't point to a source) it was, but Lee studied with Barry Strauss, who basically buys Homer hook line and sinker. Eric Cline at George Washington U. has a more nuanced view. In a series of lectures that are available on Youtube, he argued that it was historical, but it is the collected memory of some 200ish years of conflict between Mycenaean Greeks and the various populations of Anatolia.

At which point, I have to ask, are we talking about Homer's Trojan War, or is this just marketing for bronze age history?

3. What the fuck are the speeches in Thucydides? Thucydides gives a little note at the beginning of his history saying something like after interviews, reviewing what documents he had, and relying on his own memory, he produced speeches as accurately as possible, or supplied the gist of what must have been said if he couldn't collect sufficient information.

People have taken this to mean he just made up the speeches, and sometimes that must be true. He records speeches given in secret meetings for instance.

But others, like the funeral oration, would have been given in public to nearly the whole populace for an audience. Kagan thinks Thucydides is being honest and faithfully recording what he can, while filling in only the blanks. Which leaves us to sort out what is authentic and what is imaginary.

4. The historical Socrates. It's fairly well accepted that some of Plato's dialogues are representations of actual conversations Socrates had with his students, while in others Socrates is a fictional character that acts as a mouthpiece or foil for Plato's thought. Sorting out which is which is the problem.

I know a professor (left unnamed because I don't believe he published this) thinks he can tell the difference. ΄Ο Σωκράτης, with the article, being the real Socrates, and Σωκράτης being the fictional character.

I am not enough of a linguist to judge this claim.

5. Basically everything related to Alexander. We know Alexander took historians and other academics with him on his campaign in Persia, and we know some of the titles and the authors (Ptolemy comes to mind), but the first coherent history, to the best of my knowledge, is a 2nd C CE work by Arrian, so 500 years after the fact. There are also these weird Alexander romances that treat him like some sort of King Arthurish fictional character. So how do we work that out?

I'm not an Alexander scholar; I don't have any clue where to start.

So those are Lee's big problems with Greek history. I'm sure other people have other lists.

I'll be interested to see what the problems with Egypt are.