There are no spoilers in this review, just a description of my experience of reading the play.
Halfway through the play I was so excited that I made myself take an overnight intermission so I wouldn't consume the whole thing in an afternoon.
My excitement came partly from finally having something new in the Harry Potter story. It's been five years since I saw the final movie and nine years since I finished reading the series for the first time. Now here was something new but familiar, like the first episode of Star Trek TNG or the beginning of the Dark Knight Trilogy, except with J. K. Rowling's humour and emotional pull.
I was also excited by the originality of the ideas, the new possibilities that were opened up and the old certainties that were questioned. I've read the series twice. You can't do that and not have questions about Harry's relationship with Dumbledore or how other people felt about the number of people who died to save "The Boy Who Lived", or whether Hogwarts is really somewhere I'd want to send a child to. All of these are touched upon without getting into dogma or descending into insider jokes.
The next day, I finished the play and I was less enthusiastic. I enjoyed the play: the plot worked, the characters drew on my emotions and there was a lot of action crammed into a small time but somehow I didn't finish it with the high I had expected.
I've taken a few days to try and understand my response.
My first realisation was that, by the end of the play, I was mourning the 500 page novel it might have been. The novel would have given the ideas and the characters more time to blossom and have allowed more ambiguity and more room for interpretation. This is a powerful story not just of good and evil but of fathers and sons (and daughters) and how differently children and adults see the world, how hard it is, even with good will on both sides, for them to understand each other or to avoid hurting each other. In a novel, I would have savoured those things. Reading them as a play made me feel rushed to the point of feeling slightly cheated.
My second realisation was that that was largely my own fault. Way back in the 1980's, when the Greater London Council still ran Adult Education Courses that weren't vocational, I attended a set of evening classes based around Ronald Hayman's book, "How To Read A Play". In that course I learned that reading a play required me to use my imagination differently than when I read a novel. With a play, I needed to go beyond the text and think about how I would direct each scene. The script format tends to lead the reader to pay too much attention to the characters with lines but to stage the play I'd need to visualise where the non-speaking people where during a scene and what they were doing. I'd need to amplify the stage directions into something physical and something as influential as the soundtrack to a movie.
In my hunger for a new Harry Potter story, I'd forgotten everything I'd learned about reading a play all those years ago and I'd approached "Harry Potter And The Cursed Child" as if it were a novel with clumsy formatting. In effect, I failed to imagine half of the play and so cheated myself of some of its impact.
So I went back and read the second part of the play again and had a lot more fun. I still think there are points where it's a little heavy handed (but then I feel that way about a lot of plays) but the play itself works.
I think it works best for Harry Potter fans who are fully conversant with the previous seven books but with 450 million copies sold, there should be plenty of those.
If I was a more social person and a member of a book club, I'd suggest doing a read through of this play with members of the group taking particular parts. Even with an amateur sight reading, the thing would come to life in ways that only happen in your head if you read the play in the right way.
I think that, by making this a play rather than a book, J. K. Rowling has given Potter fans a much more social way of indulging our addiction. We can come together to perform or direct or light or stage or watch this play and it will be different every time. There is something quite wonderful in that.