When Harry is a first year, Professor McGonagall recommends Harry as seeker and gifts him a Nimbus 2000, breaking the house rule according to which first years are not allowed to have brooms. The idea is probably that flying (and especially Quidditch) is too dangerous, and first years shouldn't dodge Bludgers or fly unsupervised. It's allowed to fly under the supervision of Madame Hooch, on school brooms. Harry was good, but my impression was that he wasn't as good as Quidditch prodigy Viktor Krum, to justify making him the youngest seeker in 100 years.
When Harry enters Hogwarts, Slytherin house is on a winning streak for both the House and the Quidditch Cup. The Seeker is extremely important to the outcome of the game, so could it be that Minerva was desperate enough to change tactics and use a young, lightweight seeker, giving an unfair advantage to the Gryffindor team?
Later, in Harry's third year Professor McGonagall says to Harry:
"...Potter- do try and win, won't you? Or we'll be out of the running for the eighth year in a row, as Professor Snape was kind enough to remind me only last night…" ~Harry Potter and the Prisoner of Azkaban - Chapter 12: The Patronus
In sixth year Harry uses a spell of unknown origin that almost kills another student, refusing to tell the source that spell come from and if there's more such things he learned. Yet McGanagall has no intention to suspend Harry from the team.
Same with the House Cup. In first year Dumbledore awards exactly enough points so Gryffindor would win. How that's fair? It's not as if other houses were given the chance to fight Voldemort or had the cloak of invisibility.
There is a conversation in Philosopher's Stone when the trio discusses Dumbledore:
"D'you think he meant you to do it?" said Ron. "Sending you your father's cloak and everything?" "Well, " Hermione exploded, "if he did -- I mean to say that's terrible -- you could have been killed." "No, it isn't," said Harry thoughtfully. "He's a funny man, Dumbledore. I think he sort of wanted to give me a chance. I think he knows more or less everything that goes on here, you know. I reckon he had a pretty good idea we were going to try, and instead of stopping us, he just taught us enough to help. I don't think it was an accident he let me find out how the mirror worked. It's almost like he thought I had the right to face Voldemort if I could...." "Yeah, Dumbledore's off his rocker, all right," said Ron proudly. ~Harry Potter and the Philosopher's Stone - Chapter 17: The Man with Two Faces
So if Dumbledore was leading Harry and did everything to ensure he'd fight Voldemort and that he would be ready, how it is fair to award points for it?
Between Snape openly favouring the Slytherins and Dumbledore and McGonagall bending the rules and cheating do other houses even stand a chance to win?