One of the better terms I have come across for Jack Thorne's play Harry Potter and the Cursed Child is "author-sanctioned fan-fiction." It's true -- the eighth story, 19 years later is fan-fiction that has been blessed by J.K. Rowling, who also helped conceptualize it. It's safe to assume, then, that Rowling must have had the final veto when it came to the play, for she is the ultimate authority.
The first thing to do when it comes to reading the play is to not expect it to be a literal eighth story in the sense of hoping it to continue on that magical experience where the seventh book ended. The reason is simple: it's a play and not a novel. If we are to believe that the medium is the message, then it must be read differently; there will be no beautiful paragraphs describing the many eccentricities of the magical world, no third person voice to narrate what's happening in the background, no descriptions of the body language of the characters.
Ron is not funny, Hermione rather obnoxious and preachy, and Harry sounds as if he finally let the fame go to his head.
As a play, Harry Potter and the Cursed Child was quite a disappointment. The characters who I always held in the highest regard failed to move me; the dialogue lacked any kind of depth; the humour was lame and forced and the plot unnecessarily convoluted and relying on earlier tropes of reinstating the Dark Lord.
Yes it is fan-fiction, but there is some really good fan-fiction out there. Yes, given that this one was sanctioned by Rowling, it had high standards to live up to, but even regardless of that, it fails to come off as an interesting read. I cannot say about the live play for I haven't seen it, but the book was, well, quite simply, a disappointment. It doesn't read well, the actions and lines of the characters are only there for the plot to take shape, and none of it is natural enough to make us believe in that world.
The dialogues sound especially forced coming from the old characters -- Ron is not funny, Hermione rather obnoxious and preachy, and Harry sounds as if he finally let the fame go to his head. The one person that sounded somewhat OK was Ginny, and that was only because we didn't see very much of her in the series, and she seems to have developed a personality in the play. Draco has none of his old flair, and McGonagall doesn't inspire the same awe.
The new characters, on the other hand, came off slightly better, primarily because we didn't know them already, which goes to show that we can't help but compare it to the earlier books (which is only fair, considering they call it "the eighth story") -- Scorpius Malfoy is delightful, the growing pains of Albus Potter invite identification, Delphi is downright comical.
The story's premise starts on a bad note -- the dysfunctional relationship between Albus Potter and Harry Potter is not believable, and not because Harry can't be a bad father (he totally can) but because the other two children of Harry's do not suffer the same burden of their father's fame as he does. That kind of baggage mostly always comes with being the only child/son. The few glimpses we have of James Potter show him as a merry little kid, and the same goes for Lily. Unfortunately, James and Lily, despite being mentioned at the beginning, disappear later on in the story though they too could have played important roles in the story.
"Harry Potter and the Cursed Child" was like an old tape playing, the one you wish you hadn't found.
The plot might have had potential but it was seriously badly built. While in the Harry Potter series, each plot turn and twist is justified and later on tied up with the overall story, the entire story in HPCC fights for plausibility. Time travel as a main plot device had too many problems -- we really wonder how J.K. Rowling gave the go-ahead for this as it tends to rather trivialize the magical world created by her. Even if we were to take the story and attribute it to magic, there really was nothing very engaging about it.
A couple of good points though -- the relationship between Albus Potter and Scorpius Malfoy was one of the few believable things in the play. Additionally, Albus Potter being sorted in Slytherin too broke the traditional stereotype of Slytherin = bad and Gryffindor = good in the Harry Potter universe, and frankly, could have been the best moment of the play.
Harry Potter and the Cursed Child was like an old tape playing, the one you wish you hadn't found. Nonetheless, I'm surprised when I hear people of saying that it will "spoil their memories" of Harry Potter. Are you kidding me? Nothing can spoil the memory of Harry Potter and the depth and richness with which it was written, least of all a play which seems more like a stupid, alternate reality as opposed to the eighth story. Rowling may have given Jack Thorne the right to take the story in these weird directions, but the time has gone when Harry Potter was hers alone. Loved by millions of readers, Harry Potter has a life of its own, and as the message of the series clearly states, it's up to us to see the magic and believe and not be bogged down by what has been shown and given.