Unlike last week's selection I have actually used the harpy a couple times, minotaurs quite a bit, and in an old 3rd Edition campaign two players rolled up a pair of satyr drunken master monks.
Centaur
The physical description is fine--not that I assumed it would not be--but given both their mythological and fey roots, I am surprised that their personality is described as "generally mild-tempered", and that they "enjoy the studies of philosophy and arts".
The only example that I could find of a particularly wise centaur was Chiron, who was not even directly related to other centaurs. They are otherwise described as a fairly chaotic bunch, on par with satyrs, which I think better fits their fey origin anyway. It is not that I am opposed to the idea of benevolent centaur teachers (which could make for an interesting NPC), but I think it does not suit their race as a whole.
Also, why do they not attack with their hooves? Not only has the hoof attack been part of them since at least 2nd Edition, but I can easily imagine one pinning a creature under its hoof and then, assuming it is not dead already, finishing the job with a sword or arrow to the face.
Satyr
The description for satyrs is almost spot on (despite more accurately depicting fauns, which 2nd Edition mentions as an alternate name for them).
My only criticism is that I would make them capable of weaving magic into music without the need for enchanted pipes, giving them a natural knack for whatever amounts to bardic magic. Keep magical pipes, just as an interesting item and not a necessity. Like angels, I would also prefer that their magic is not directly mimicked by spells (though a set of thematic spells could also be cool).
As for female satyrs, well, in Roman myth the gods Faunus and Fauna were male and female goat-people respectively, and satyresses were also apparently a thing, but it is not like I expect Dungeons & Dragons--which has stuck with male-only satyrs with the appearance and pan pipes of a faun for quite some time--to adhere closely to real-world mythology.
I want them to come up with interesting, hopefully compelling flavor material, and I can see an argument for both sides.
Harpy
I am curious as to why, given that originally harpies seemed to have the bodies of beautiful woman, that Dungeons & Dragon's makes them ugly. From what I gathered harpies do not even have a luring song; that feature belongs to another bird-woman hybrid, the siren (also the basis for the Russian sirin), which came in a variety of depictions depending on the bird-to-woman ratio, but was still described as beautiful.
As with the satyr, I am not expecting Dungeons & Dragons to stick to the mythology, but instead use it as a basis for creating awesome stuff. Personally I think that the appearance of the original siren is more interesting, though the more divinely oriented sirins, which had bodies of owls and sung songs of future joys to saints, could make for an interesting counterpart to the "classic" evil and hideous harpy.
Minotaur
Why not have minotaurs be a race created by Baphomet, with the really big ones those he has specially blessed/cursed? Why not have ogres be the Large, savage ones, with humans accounting for the Medium-sized, more civilized crowd? It sounds better than them size-dropping like Mario just because they got smarter.
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