When it comes down to it, the reason I didn't enjoy this was because it didn't feel like an authentic continuation of the Harry Potter novels. Here's why: 
 1) While there are some similarities - both Harry and his son struggle with fitting in and loneliness and feeling orphaned - the main themes are hugely different. This is very much a generational story focusing on relationships between father and son. Which means... 
 2) There is almost no magic of Hogwarts here. There is no whimsy. The adventure and the spells are not as exciting as they used to be. There is some humour, but nothing like the dry, sarcastic humour of the novels. When there is a funny line it can fall a bit flat. This may be due to... 
 3) The format. I'm not against plays, but as so many have said before, this would have done SO much better as a novelisation. The play format does not allow us to properly get into our characters heads, we lose out on J K Rowling's exceptional writing style, which is just depressing, plainly put. And speaking of characters... 
 4) The characters are no longer recognisable. This is the worst part, for me. I mean, we see Harry, Ron and Hermione together again and I was initially thrilled. But they're older, and they have changed. Harry is a Ministry man and is struggling with fatherhood. Gone is his recklessness and his kind of obnoxious bravery. Hermione is mostly still Hermione but makes some decisions I cannot understand from her. And Ron - Ron is reduced to comedic relief. Sure, he had that about him already but he also had courage and jealousy and awkwardness and a heap of other things. Now, he's court jester. We also meet... 
 5) The new characters, Albus and Scorpius. We also meet James, Lily, Rose and Delphi. All a new generation. Albus and Scorpius, being the leads, get a lot of screen time and are pretty well developed, but can't even begin to reach the level of their predecessors. Maybe it's because of the format, because of the shorter length, or because we could never love anyone as much as Harry, Ron and Hermione. And where on earth is Teddy, the son of Remus and Tonks? And this brings me to my last and most important point... 
 6) The plot. THE PLOT. By itself, if there weren't 7 books, 8 films, a whole truck load of fanfiction, Pottermore, fansites, illustrations, basically every Harry Potter fan ever picking the books apart and knowing them back to front, it might have been good. It might have made some sense. But now... (view spoiler)[ we are expected to believe that Voldemort had a child with Bellatrix?? Really? This does not sit well with me. This was clearly not pre-meditated, and this obviousness destroys this for me. J K Rowling was always such a careful planner and by the end of The Deathly Hallows everything had been tied up so neatly with such cleverness. This, by contrast, reeks of a 'what-if' idea in an AU Universe that I would expect to see in fanfic, not in a CANON SEQUEL. (hide spoiler)] 
 But, I gave it 2 stars for a couple of scenes I enjoyed. Mainly, the darker ones, where we meet (view spoiler)[ Severus Snape, still undercover in a Hogwarts ruled by Umbridge with mudbloods being tortured in the dungeons. I very much enjoyed his reaction to being told of his own demise. (hide spoiler)]. Also, I liked Scorpius and Draco. 
 For a continuation of Harry Potter, it feels very little like a true continuation. It does not feel authentic, it raises many more questions since all the answers had been taken care of, and if I consider it canon, like I should, it weakens the Harry Potter series for me.