Hmmmm. . . . I don't think I'm very fond of this book. Though it had some wonderful moments of gem-like perfection. . . I don't think it worked as a whole.
Scorpius was good. I'm particularly fond of the line: "I, uh, I opened a book. Something which has — in all my years on this planet — never been a particularly dangerous activity." (Though I can't figure out for the life of me why he ended up in Slytherin.) Snape had some of his finest moments in the series. Draco's character grew from the flatness of the books. How Scorpius and Albus communicated with their parents.
But it hit a major dislike of mine: it undermined the happy ending of the book before it. It also demonstrated the problem with theater and prolonged periods of time, with the compression of their first years not working well. (That it necessarily needed to have fewer characters also did not help.)
And, well, Delphi.[Spoiler (click to open)]I can imagine a scad of reasons for Voldemort to have a child. Each one more selfish than the last -- to use part of her in a spell as he used his father's bones, to anchor himself to time -- perhaps early in his career, he might have seduced a woman as the easiest way to get what he wanted, or to test whether he was immune to seductive magic she used -- perhaps to manipulate a follower, though as his treatment of Draco shows he was weak on that sort of thing. Unfortunately, you really need to give some kind of motive. It seems kind of fan-fic like.
Not so good as the books.