Harry Potter is not a good example of a Mary Sue (or Gary Stu). Hermione on the train is far more advanced that either Harry or Ron, and, as a Muggle-born she’s had the least amount of guidance. Harry has a few accidents when he comes to his abilities, but that seems to be typical when new wizards come to their abilities.

I think a good example of a Gary Stu would be Wesley Crusher of Star Trek: The Next Generation.