I did enjoy this very much and I'm dying to see the play. I want to explain why, but first of all you need to know: 
 1) I was a huge HP fan, I know all (?) there is to know about the HP world and its characters, and these books were a huge part of half my life, but I considered myself to be over it when I got this book (I kidded myself into thinking I was too old to be still obsessed with HP), which means that I am ZERO OBJECTIVE about this play BUT ALSO that: 
 2) I had no expectations at all when I picked this up. I knew it wasn't written by JK, I knew that although it was canon, it was not an 8th novel and whatever I didn't like I would pretend I hadn't read. I think this is important, because although you might have high expectations on this, you need to realise, before reading it, that it is not more of the same, it is not a continuation and (although it might seem impossible) you cannot judge it by the books. 
 (also, 3) I used to be OBSESSED with Cedric Diggory (long before Robert Pattinson, of course, although I did became a fan of him despite of the disaster that film was long-long before Twilight), all my fanfics (did I say HUGE FAN) were about him and all my passwords and nicknames included something Diggory related), so every time the name "Cedric Diggory" got mentioned in this book, the fangirl in me swooned and I became even less objective). 
 That said, and admitting that there are problems with this play (there are several, mainly plot-related, I'll put them afterwards under "spoilers"), I loved it loved it. I laughed and cried the whole time. In fact, I started it on the train on the way home and had to hold myself from laughing, so I think I made some pretty weird faces. I read the next 70% at home, so I could cry and laugh at leisure. I recommend you do the same. There are some adorable characters and the dialogue is wonderful, smart and witty and silly at the same time. I fell (like the rest of the universe) for Scorpius (and also for Draco, I liked how he was done, realistic but sympathetic) and liked the portrayal of Albus (which was in fact very Harry-ish in his egomania, I liked how Scorpius called him out on it), I adored Hermione, Ron (albeit his silliness, it was fun, alright? As Scorpius would say "he's a funny guy" (HOW I laughed at this line, at the precise moment it was said)), Rose, McGonagall, Ginny, and even Harry. Some people say this reads like fan fiction (and they are not wrong) as if it were an insult, but the fact is that fan fiction can be wonderfully amazing. 
 Now, to the things I did NOT like: (view spoiler)[ 
 1) I won't deny the whole Voldemort-has-a-daughter plot is incredibly silly. It completely is. I never imagined him, in his Voldemort-stage (especially 5th book onwards) as an actual human being, I truly do not believe him capable of procreating (nor having sex, to be honest). But IT'S FINE! LET'S JUST ACCEPT IT AND MOVE ON! 
 2) The time-turning concept in itself. I cannot accept that such a device exists (more than one, in fact) and that it would only take one silly mistake in the past to make this a Voldemort-dominating world. It is silly and irresponsible. And the whole butterfly-effect thing was taken to another level. 
 3) Did I mention I used to be obsessed with Cedric Diggory? That means I got extra emotional when I realised what the plot was about (TO AVOID HIM FROM DYING), but that I was extra angry that somebody would think Cedric would become a Death Eater just because he was (greatly) ridiculed in public. C'mon. How can you go from him being an amazing person who could probably had been a famous Quidditch player or an Auror (the play's words, not mine) from being a Death Eater? Aren't there greys in this world? 
 This as well as other things: Yes it is silly that if Neville didn't kill Nagini nobody would, or the idea that Ron fell in love with Hermione when he got jealous at the Ball (he realised he felt something for her, he didn't actually fall for her out of jealousy, c'mon!), among other things. (hide spoiler)] 
 This is mostly it, although it also bothered me that James Sirius and Lily Luna weren't more in this, or that neither Teddy or Victoire were in it AT ALL. All in all, however, I accept all the silliness for the sake of the play itself, because it had to move forward and I liked how it did. I enjoyed the general plot (Albus/Harry), how it was written, and, most of all (this might be the key to like this), I didn't take any of it very seriously. I consider it cannon but from a parallel universe, you know? Remember, the important thing is TO JUST ENJOY IT!!