Most of the teachers? Binns and Trelawney certainly, Snape, but arguably he's more unprofessional and unpleasant than incompetent. Often the defense professor is incompetent, I suppose. Canon!Harry had Lupin, Snape and fake Moody for competent defense professors and Quirrel, Lockhart and Umbridge for incompetent ones. We have no reason to doubt the teaching ability of Mcgonagall, Flitwick, Sprout, Sinistra, Vector or Babbling. Burbage's Muggle studies course is often a subject of ridicule in fanfiction, but that might be a result of the (inter?)-national curriculum rather than her individual competence, and so would be no better at other schools. Hagrid's Care of Magical Creature's lessons were of very uneven quality, but he could teach well when he had his head together.
As to the preeminence of Hogwarts, perhaps its as simple as Hogwarts being the only British school with a comprehensive curriculum, the others focusing on particular areas of magic and functioning more or less as magical trade schools. We don't technically know that there's no entrance exam for the common witch or wizard, we just know Harry didn't have to take one, he could have been admitted as a legacy student or simply because he's the boy-who-lived. Or the barrier could be financial.
(The HPMOR discussion thread after this one is here.)
The previous thread is over the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread. This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it. The latest chapter as of 09/09/2011 is Ch. 77.
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight. The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: