I shall try to review this book without spoilers - by focusing upon its form and the impression it made upon me, rather than the specific content.
Overall, I would say that the book is OK; but unimpressive and underwhelming - I was never at any point grabbed by it, and had to push myself to continue reading.
(This was not because I am unfamiliar with reading plays in script form - in contrast I have read hundreds of modern plays, for my own pleasure or interest - e.g. nearly all of the canonical plays of the British theatre from Shakespeare's time, including all of GB Shaw, and most of the mainstream published British plays from about 1945-80.)
Like most popular theatre throughout history, the script for Cursed Child is at the level of farce and melodrama; and did not at any point rise to comedy or tragedy. The prose is merely functional (considerably below the quality of the Harry Potter novels), and never poetic - and it is only by poetic qualities to its language that a play (qua play) can rise above farce/ melodrama.
Aside, the vast majority of plays achieve their higher or deeper qualities by factors of the production rather than by their words - i.e. the special qualities of acting and stagecraft (plus topicality and novelty) - or by the working of music, in the case of musicals and operas.
In sum, the most impressive factors are usaully extraneous to the writing. and confined to the live performance situation and thus do not long survive -- Which is why the permanent literary canon of plays is so slender compared with that of poems or novels; and also compared with the vast number of plays that are - for a while - a popular or critical success.
http://charltonteaching.blogspot.co.uk/2010/11/drama-is-nearly-all-ephemeral.html
The best way to approach reading The Cursed Child is to think of it as a dramatised Soap about Harry Potter et al; or as a canonical Fan Fiction - because its focus, scope and nature is most like FanFic. I mean by this than FanFic is mostly about 'shipping' or relation-ships, and takes a strategy of getting the characters and making them a different age, or putting them into a different setting, or taking minor characters and making them protagonists - which is what Cursed Child does.
The Soap aspects are dominant because Cursed Child is utterly without the underpinning spiritual, indeed religious, aspects that raise the Harry Potter novels to the level of works of a work of genius.
The highest point to which Cursed Child rises, is the level of interpersonal relationships considered from a 'utilitarian' ethical perspective - of that being best which makes the most people happiest for most of the time, and especially that which minimises suffering. From this angle; there are several heart-warming moments - as well as several more unconvincing, contrived and clunky male-male interactions.
The 'moral' of the two play cycle (as it came-through to me) is superficial and implausible: that evil is caused by childhood loneliness. In other words, the plays have a very secular, modern 'psychodynamic' kind of ethic (whereas the moral of the HP novels was very traditional - that the most important virtues are Love and Courage; and their importance goes beyond mortal life).
So - should you read it? That depends.
If, like me, you found the Harry Potter novels to be a deep experience, then probably better not to read it; because this book may tend retrospectively to trivialise and 'poison' some of the best aspects of the novels (in the way that a movie of a book more often does).
If, on the other hand, you regard the Potter novels as mainly about human relationships and intricate plotting, then the plays would probably be of interest.
And if you are a Potter FanFic writer or aficionado, then you will probably be this play's ideal audience.
