How does magic work in the world of Harry Potter? If potions work despite science saying they shouldn't, what makes potions work the way they do? What makes a wizard powerful or weak, and what makes a wand powerful or strong? If some wands are better for delicate tasks and some are better for raw power, why not carry multiple wands for different jobs? What exactly makes a wand "Just right" for a wizard? Is there some benefit wands get for looking like costume store-bought garbage and not something more precise like a pencil with magic animal core as the lead, or inside the lead? How do wizards that turn into animals control their new animal bodies? If all it takes to teleport somewhere is to focus hard on somewhere, why save it for the final books when single-minded focus is such an easy skill to develop when needed?
How did a wizard with Voldemort on the back of his head make it into Hogwarts? Why is the Vanishing Cabinet even there? How do runes work? How do you learn and master the art of runes? Why is Hogwarts, "The best and safest school in magic britain", ok with having terrible Defense Against The Dark Arts teachers when "How to fight enemy wizards" is one of the most important subjects magic kids after a war could possibly learn? What makes Harry's invisibility cloak so special if others exist, yet all are equally invisible and this is just "The special one" for never running out of charge or some such BS? If "Charms" exist that can make objects dance, do those spells make the objects sentient/sapient and give them orders, or just control all limbs QWOP style? Are Wizard Chess animations programmed, or generated by semi-living golems? What has the world decided when it comes to the morality of turning animals into objects and objects into animals and people into objects? Why does nobody ever think to transfigure people into objects?
This is a world where mindreading spells and truth potions exist. Why would trials be necessary when the truth can be magicked out of people? Have people decided the previous question's answer is "Shut up because morals", and if so, why doesn't this apply to anything else?
Is magic ability really determined by "Blood purity" (Genetics) or not, and if so, what is the magic gene? Can it be spliced into people or babies? Is it determined by how much you study? How much you believe in yourself? How much you want the spell you're casting to succeed? Your feels? Your ability to see the beauty in things? How much you've exercised? How much food you've eaten recently? How good your bootleg chakra network is?
Did Dumbledore inspire Voldemort's turn to the dark side when they first met?
Where do Dementors come from?
The wizarding world was more prepared for students using magic to impersonate an older student to get into the Goblet of Fire than it was for a student asking an older student to put his/her name into it. Why?
If there are magic potions that heal you, why not carry multiples around? If Voldemort has all his followers get a magic tattoo, why do none of the good guys ever think to say "Right, you look cartoonishly evil. Strip down, and show me if you have the Dark Mark or not". If the evil magic tattoos can be used to communicate with followers of Voldemort and torture them if needed, why do the heroes never think to hack into this, initiate hypertorture, and use freezing spells on anyone that starts screaming?
If you can edit or erase the memories of others, why did nobody ever think to edit the memories of Neville's mindbroken parents? Can't be mindbroken from getting tortured to insanity if you don't remember the torture happening or know why people look at you in surprise when you walk out of St Mungo's.
If luck potions and "Victory potions" exist, why is their creation not a closely guarded secret? And since it's not, why are they not abused to hell and back? What happens if two people down those potions and fight each other?
How do "Anti-cheating charms" work?
If you can enter someone's name in a magically-binding contract hat thing and force him to take part in a potentially-deadly tournament, why did Voldemort never exploit the crap out of this, having members of the resistance and random innocents fight in The Hunger Magigames for the lulz, mages easily taking out the one remaining member of a resistance/order that was 10/20/100 a few days ago?
If you can Transfigure objects into anything you want, ignoring the laws of equivalent exchange because screw balance, making you Edward Elric but with infinite philosopher's stones, why has nobody ever thought of exploiting this? Can you Transfigure fake or fictional or imaginary objects you can visualise well enough? Partial Transfiguration is supposedly impossible, so how have children accidentally pulled this off in-story? If someone studied hard enough, could he/she use and master partial transfiguration? Could a Wizard Transfigure a handful of marbles into living Pokemon? Could a Witch turn two fake nails into Uzis and open fire? Why has a Wizard never tried transfiguring his glove or bracelet into an armoured hand covered in ultra-long ultra-sharp spikes to pierce through attackers still trying to pronounce magical words? Is transfiguration the origin of Magical Creatures?
Could a Wizard's patronus be a fictional creature, like a Pokemon? What happens when it is?
Can you use memory-editing spells to make someone think he just memorized 40 books of magical information in an hour, like putting an image full of text into a powerpoint slideshow? If not, why?
Why did Dumbledore let Sirius get sent to azkaban without trial and get tortured for years, and why did nobody ever really call him out on this? He's the "supreme mugwump", whatever the hell that means. What happened to all the power this number one wizard supposedly has? For a good guy, he sure is terrible at the whole "Be a good person" thing. Inb4 "He thought Sirius killed his buddy for the lulz, so he never bothered to demand a trial" or "It was necessary to his plan, and being the good guy lets him be the world's worst good guy because muh hero license!".
The Weasley's magic map, which was created by The Marauders, is powerful enough to detect Harry even when he's under "The special invisibility cloak", the one that was so special, it could somehow let you hide from death, as if he's a real person floating around looking for people to kill.
That alchemist and his wife mentioned in the first book, how did they live to be 800-and-something, and why was this technology never replicated? If 30-40 years of practice and study can potentially make you a Professor-tier wizard, what can 800 years of practice and study do?
After all the BS transfiguration can canonically make, why can goblin coins not get magically forged?
Despite all the many ways to carry out murder and get away with it, why are there any wizards left standing, and why do break-ins and murder-thefts not happen more often?
What makes a spell "Dark"?
How did Voldemort get so ugly?
If Bogarts can turn into your worst fear, what happens when one is shown to a kid whose father died during the war, a kid whose worst fear is Voldemort? What if a Bogart is shown to a kid whose worst fear is some unkillable unstoppable horror movie villain, or a concept like total atomic/nuclear annihilation? What are the limits of this creature and its ability, and if memory-edit spells exist, why has nobody mindscrewed somebody into fearing magical cows that give infinite milk and shit oil and feed off sunlight, then showing a Bogart to him and capturing it after it transforms?
Why are parents alright with it when Snape bullies and mocks students for screwing up potions spells, students that are often children? Why did nobody point out that he chose a suicide mission as a mediocre spy to get the chance to be a dick to Harry, when he instead had assloads of potion talent and was able to correct textbooks he never bothered to correct upon becoming an adult, intentionally teaching kids with bad textbooks and blaming them when things go south?
If the process of becoming an Animagus is so hard and so government-controlled, why isn't it mastered in secret more often? And if Pottermore is to believe, how hard can it really be if all the kids in [Insert ethnic school containing ethnic group Queen Ripoff was trying to pander to here] can turn into animals by the time they're ten?
If you can edit memories, why does nobody ever try to create fake memories in people to manipulate them?
Broomsticks. How do they work?
Why are tactics used so rarely in this world?
Voldemort would still be semidead if his followers were not around to revive him with that stupidly complex Goblet Of Fire plan. Why does nobody notice this, ever? Why were convicted Voldemort followers allowed to get off scot-free despite their crimes, just for saying "Magic Hitler made me do it"? If that shit didn't fly at the Nubenberg trials, why did it fly for Wizards?
The dark forest. Dangerous place. Forbidden for kids to go near it. Except when it's used for detention with the least magically powerful guy in the whole school. Where's the logic here?
Why is wizarding society so corrupt and morally bankrupt? Why is the Ministry so corrupt? Why do people put up with the corrupt Ministry? Why were people cool with it when Harry, underage at the time, was put on trial and tried as an adult for defending Chungus McFatface from Dementors that were "Under Ministry control"? Why did Dementors "Under Ministry control" attacking people raise no red flags? Why did Harry never object to the fact that Dumbledore chose to put Harry not with a loving Wizarding family ordered to tell Harry nothing about magic, not with a muggle family paid to adopt him and treat him well, not with a mindwiped family of muggleborn wizards, but with Harry's abusive aunt and uncle? Why is "Well I didn't want you to get a big head, you'd be less heroic and harder for me to manipulate than you would be if I presented myself to you as a wise and all-powerful savior" considered a good enough reason to put a child in an abusive home and let all kinds of bullshit happen? It'd be a stretch if Harry decided the Wizarding World wasn't worth saving and buggered off over to America to live out his days in peace while England went to hell, but why does he never once notice or question any of the bullshit that happens in these overhyped poorly-written books that pretend to be far deeper than they actually are, especially the bullshit that only flies because the writer needs it to fly for other bullshit to fly?
These are world-building questions the writer needs to answer in his/her books, not tell me the exact year in which Flingley Stindleflemben invented the Plumbus or Vomiting Draught and how many years it took for his son, Grimsby Stindleflemben, to refine the design/formula, or how many should-be-illegal things The Obligatory Prankster Characters sell in their joke shop. The writer uses pointless infodump after pointless infodump and stupid "Hey kids did I mention we're in a kid's book?" after "Omg we're like so dark and goffik and edgy and cereal right now" moment to distract readers from all the bullshit in these books.
And no, hoping your fans think of bullshit to justify bullshit or accept the bullshit and demand others do the same is not the same as answering these questions. Worldbuilding is meant to make the world feel like a real place with internal consistency, not something you do to show off your ability to put fake-latin words and silly names and silly concepts and stolen ideas on a page.