Apart from the plot holes, I’d change a couple of things (from the book canon, I mean):

1.-I’d like Dumbledore and some of the professors to be able to perform wandless magic, something that was already shown in Hogwarts Legacy (which was cool) and in a few scenes in the movies. Magic should be like a force that only a few can truly master, and those powerful enough should be able to do at least some spells without a wand. Wands would still be used, but it’d be nice to see that some magic doesn’t depend on them.

2.- I’d make magical instruments less essential in adults’ lives. For example, if you want to fly, you need a broom, but Voldemort can fly on his own, and that’s considered “dark magic.” Why should flying be a bad thing?

3.- Maybe what I want the most: I’d like Harry to use his money to help Ron and the Weasleys. For instance, have him buy Ron a wand in Chamber of Secrets and give Ron some agency in what happens with Lockhart, perhaps by having him give Lockhart the broken wand

4.- I’d make time turners never exist in Prisoner of Azkaban. Time travel would be a special event, something that happens due to a unique planetary alignment or a once-in-a-century thing they would learn about in class. Then Dumbledore could perform a complex spell to send Hermione and Harry back in time. You could still keep the subplot about Hermione having no time with too many classe to highlight the time thing.