Read the document.
Here we go:
1) Document Length: a six page document is not a Design Document. It is called a high concept or treatment at best. If you are designing any game it should take about 20 pp. Any less and it is impossible to fully detail what the game should look like and play like.
2) Overview: Says nothing about the game. Says alot about HP (please see my post above about illegally using IP) but nothing about gameplay. As others have pointed out, this line "the player will also be able to use magic at any time, and as the game progresses, the
character will learn new spells." is saying nothing more than what happened in the book; it doesn't point towards any original or derivative gameplay.
Furthermore, here you repeat yourself "[...]character will learn new spells. During his time at Hogwarts, he can explore the whole castle, learn
new spells in fun mini-games and brew exciting potions." and once again state you will learn spells and brew potions.
The reader at this stage has the following question: what is a special about your game? From your description, it sounds exactly like the HP games that are already out there.
3) Characters: this is fine for a high concept, but not enough for a design document. In a GDD, you would go into more detail on each individual character. You say you can play HP... well so far I still don't know what the gameplay is!
4) Plot: please see my warning about IP. You CANNOT use the IP story nor modify it for your own projects, even if free or fan based.
5) Locations: This is actually done well. Sticking with only the first book gives you a realistic set of locations. However, you need to describe the locations better. Are you doing the whole castle, or just bits. ARe you doing all of hogsmeade or just the Boars inn...etc
6)Mini Quests: there is some problem with language. You refer to the below categories as mini quests but then talk about mini games. Never include something in a design document that isn't referenced somewhere else. AS others have point out, you've made a passing nod to a "lessons mini game" but have no solid description of what that is. It could be a multiple choice test, it could be a tetris game, it could be anything and a design document is supposed to be so it's not anything, it's something.
(EDIT: confusion. Your organization on this section is poor. I don't know if the mini quests are lessons and quidditch or what. After reading through a few times I get it, but trust me, people will not spend this time trying to decipher what you mean)
6.1?) Lessons: as others have said, you've made no mention of what this game will play like. You state how to make a potion (get recipie, gather ingredients, make potion) but that is not a game, that's a description from the book! I'm afraid all your lessons suffer this problem: they describe the actions as per the book but give no equivalent gameplay descritption. It's fine to know how they do it in the book but that has nothing to do with how you want to do it in the game.
6.2?) Quidditch: I'm assuming quidditch is the second mini game. Here again, you mention the game as per the book but no mention of how we will play it in your game.
7) Collectables: I don't know if this is a miniquest or not, but what do these collectables do in the game? For example, gather the pieces for the wizard chess game. Can you then play wizard chess? It's not mentioned anywhere so I don't know!
Conclusion:
This is not a design document. And I will leave you with the main reason why: after reading the entire things, I STILL don't know if this is a RPG, FPS, RTS, Action, Adventure, what! I have NO idea what type of game it is! I know I play HP, but that's about it. As well, there is not even a keyboard map. Something as simple as arrow keys to move, "i" for inventory, "r" to run, etc not only solidifies your gameplay but also gives insight into the type of game (a RPG will have a different keyset than a RTS and FPS, etc...).
Recommendation:
1) create a 5 minute walkthrough. Describe what the player would see and DO in teh first five minutes in the world. This is also a good oppurtunity to hash out a tutorial. The walkthrough will give everyone a better idea of what the game will play and look like.
2) Choose ONE location and ONE character and ONE spell and ONE lesson and ONE...etc... and develop that and that alone. Ignore the rest of the HP world (as a matter of fact, ignore HP all together) and focus only on ONE thing to fully detail what your game would be like in this limited instance. Once you've succesfully done that (success means that a person can read your description and know how the game will play)
