Introduction: Hogwarts is the school mentioned the most in the series. It is the only school we see the inner workings of. By no stretch of the imagination, it also has its issues and could do with a major overhaul in various places. I shall list everything I think could do with an improvement or change in Hogwarts. I admit there are probably some parts I haven't mentioned /noticed. Feel free to give me helpful advice.
1) Accommodation.
Hogwarts is a boarding school, with students allowed to go home during the Christmas holidays and having to go home during the summer holidays. Most students are happy to go home, but there has to be some that would rather stay at Hogwarts, or at least not go home, during all the holidays.
Three students known to have reasons to not return home are Tom Marvolo Riddle (raised in a muggle orphanage and not happy about it), Severus Snape (in his memories, we see his parents arguing, and he tells Lily about them arguing a few memories on), and Harry Potter (raised by his muggle relatives and treated like a house-elf).
While Hogwarts is a school, it has a duty of care to its students. I can’t think of any country where a Headmaster is allowed by law to choose where the son of former students (who will later become a student) grows up after the parents die. Nor is the Headmaster allowed to send a student back to a house where the student has asked not to be sent without investigating why the student doesn’t want to return.
2) Sorting & favouritism.
Students are placed in a house, which defines the expectations placed upon them. Ravenclaws get top marks; Slytherins become evil; Gryffindors run headlong into situations before thinking it through; Hufflepuffs… Well, they exist. The teachers react accordingly.
Due to the implied evilness in each Slytherin, it becomes a self-fulfilling prophecy. Suppose you’re told often enough that you’re going to be evil, and your classmates from other houses (and some of the teachers) treat you like you’re an up-and-coming Hitler. In that case, chances are you’ll join the biggest, meanest person around to try to get back at them. This fuels the “Slytherins are evil” stereotype, continuing the vicious circle.
While all teachers have favourites (any teacher who says they don’t are lying or haven’t picked their favourite yet), they don’t have to shove that fact in everyone’s face (yes, this is a dig at Professor Snape). While he may be trying to show the Slytherins that there’s another option, blatant favouritism doesn’t improve other students’ impressions of Slytherins. McGonagall is said to favour Gryffindors, but she doesn’t announce it to everyone, and at least she TRIES to be fair. Professor Snape… Well, fair isn’t the word that springs to mind.
This pales under the favouritism shown by the Headmaster. He makes sure Gryffindor wins the House Cup in First Year, to the detriment of a quarter of Hogwarts (who aren’t going to be sending him Christmas presents anytime soon. Unless they’re cursed presents, of course) and Harry Potter spends so much time in the Headmaster’s office (compared to other students), he may as well move in.
3) Employment.
Hogwarts has had some horrible teachers (I’m not going into the stream of useless DADA teachers). Trelawney seems to think it’s her mission in life to predict horrible deaths for everyone, Binns is determined to bore everyone to death, and Snape wants to scare everyone to death. It’s a miracle Hagrid’s classes only resulted in a cut forearm (is he a nice person? Yes. Is he a teacher you’d want teaching your children about potentially dangerous creatures? Depends on how much you care about said children’s lives), and Hooch, no matter how enthusiastic she is, still left a group of 11-year-olds unsupervised with flying broomsticks after one student broke his wrist.
We may as well fire Dumbledore for hiring all of the above. Other things to add to the list of offences against him are: endangering the lives of the students; hiring criminals (Snape, Lockhart and Barty Crouch Jr); allowing dangerous creatures inside the castle (Fluffy, we’re looking at you); and hiring someone unapproved by the Ministry (no matter your opinion on the topic, he still broke the rules by hiring Lupin. There are other ways to stand for werewolf rights that won’t result in student deaths if Lupin forgets to take his medication).
Also, dear readers, if you could cast your minds back to secondary school/middle school/whatever word your country of residence prefers to use, would I be correct in assuming (for most people) that A) there was more than one teacher for each subject, B) there was a way to find substitute teachers if one of the resident teachers were unwell, C) your school wouldn’t allow dangerous animals on campus, untrained government officials to teach, or potentially life-threatening inter school competitions to take place, and D) teachers weren’t allowed to insult their students in every class, no matter how much damage could have been caused by a student not paying attention?
Hopefully, I’m correct, and most countries would have had an issue with everything that happened at Hogwarts. If not… well, just be glad that Hogwarts wasn’t your school. The government in your country of residence probably wouldn’t have cared if the whole school was blown to kingdom come.
4) Dietary requirements.
Hogwarts meals are renowned for having a wide variety of options. If it was a restaurant, it could be one of the best. However, most of the food will be consumed by 11 to 17-year-olds, who aren’t renowned for their brilliant choices. While there are undoubtedly healthy options available, most children will ignore them, reaching instead for foods high in sugar, fats or carbohydrates, which, while OK in moderation, aren’t beneficial in large quantities.
Without a mandatory exercise regime (playing Quidditch every odd now and again ISN’T exercise), it’s a miracle more children in Hogwarts don’t become obese. Choice is good, but make them eat the right foods for their age, gender, metabolism, and exercise levels, and no more.
5) Cleaning.
Hogwarts is a large castle. There are multiple floors, classrooms, statues, armour stands, trophies, plaques, and unused rooms, all of which need cleaning. I wonder which idiot had the bright idea of leaving all that work to a Squib who can’t use magic to speed everything up?
True, the house elves do a large portion of it, and he is helped by students serving detention, but when they are banned from using magic due to the detention, it doesn’t help Filch much. Wouldn’t it be easier to hire witches or wizards as an on-site magical cleaning company? It may be more expensive, but at least they might have a hope to get all the cleaning done.
6) Slavery.
Yes, house-elves want to have a master/mistress. Yes, they want to do work. But does that mean you don’t pay them for it? Even if they protest, just pay them something. Maybe open up a Gringotts account for them or something. After all, they do all the cooking, kitchen personnel jobs, laundry and move all the luggage at the beginning and end of the school years.
If Hogwarts is a school, why is it teaching such outdated ideas?
7) Curriculum.
Hogwarts has a Muggle Studies class, but why doesn’t it have a Wizard Studies class? Maybe just in first year for muggleborn and half-blood students raised by muggles, it would teach wizarding customs, culture, terminology, government, laws, and the locations of other wizarding communities.
A new class could teach household charms to both males and females. This would allow both genders to use magic effectively when cooking, cleaning, washing laundry and other household tasks. It could also teach them charms and jinxes to protect their house from unwanted creatures, attackers, and unwanted/unknown visitors.
8) Promotion.
The last time I checked, murdering a teacher doesn't result in being promoted to their post (Headmaster Snape, anyone?). Also, teachers can’t just promote themselves in the job or use their government connections to ensure their promotion (Umbridge. Who else?).
9) Rule Breaking.
Sirius Black almost got Severus Snape killed when he "accidentally" tried to introduce him to werewolf-Lupin. Snape only survived because James decided he didn't want Sirius to end up in Azkaban (that plan didn't quite work out). In most schools, one student trying to kill another would result in a harsher punishment than detention and telling the victim to keep his mouth shut about the incident.
Harry Potter and his group of friends break multiple school rules. Out after curfew, setting a teacher's clothes on fire, hexing a classmate, entering a forbidden area - if they were anyone else, they would have been expelled before their 2nd year. Yet, even when Harry attacks a student, which could have resulted in his death if a teacher hadn't saved him, Harry only gets detention (admittedly, for a long time).
Not that Filch's preferred methods (corporal punishment) should be allowed. At the same time, punishments are supposed to deter unwanted behaviour, and Harry and his friends go out after curfew multiple times.