To expand on that - BEWWARE, SPOILERS AHEAD - there's a bunch of stuff that I've already seen in fanfiction: Albus being sorted into Slytherin and making friends with Scorpius, Scorpius having a crush on a disdainful Rose, the next gen kids clashing with their parents and not being their parents, Voldemort having a daughter, time travel to try and fix things - but to be fair, most of those are fanfic tropes I like. However, the old 'going back in time to fix things often ends up messing up the present' is predictable and as to Voldemort having a daughter... I get the theme, that it's about family and everything going in a circle, as Harry is unable to save his parents so Voldemort's daughter is unable to save her dad, and about not standing alone and all that jazz. But. I think it would have worked better if instead of Voldemort's daughter we'd have had, say, the child of a Death Eater killed in the Battle of Hogwarts, or something 'found family' rather than actual family. Something a bit less direct.
I also wasn't keen on McGonagall using the map to spy on students at a parent's request and I'm not convinced about the idea of Cedric Diggory - the guy who believed so much in fairness that he gave Harry the hint about the egg in the Tournament - becoming a Death Eater in an alternate furture just because he was humiliated during the Tournament.
I did like the old folks' home for witches and wizards, where people just do magic for fun, the theme of no one standing alone, Hermione weaponising her library, that Snape gets to kind of posthumously comment on his own death, some of the I-missed-those magical turns of phrase, the humour...Ron and Scorpius get some especially good lines. Overall I did enjoy it!
I've spoken to a few people now who've managed to see the play - who going in were in kind of the same place as me, who used to write fanfic and love the books, but are no longer hugely invested if a touch nostalgic - and they rate the play really highly, so there's that :)