After seeing it raved about by a rather stunning number of people on LJ, Usenet, and elsewhere online, I have read a fair amount (8 chapters) of Harry Potter and the Methods of Rationality. My thoughts -- which will naturally include spoilers -- follow.
Harry Potter and the Methods of Rationality is a very ambitious fanfic indeed. In fact, it is an attempt at an AU -- Alternate Universe -- Harry Potter told from the very beginning, and as with many of the best stories, takes a single change as the departure point: specifically, What If Harry Potter's adoptive family were, instead of being the most self-blindedly and determinedly ignorant sort of people, the most determinedly rational, logical, and educated sort of people?
With that start, it appears to attempt to (mostly) adhere to Rowling's basic setup otherwise (with, I am guessing, at least one major change -- see later). This is, as I said, a tremendously ambitious fic, and a very demanding one to pull off well.
Fortunately, the author has what it takes to make such an attempt without humiliation. Speaking as a published author, this is an extremely well written fic. I hope that the author (who goes by the name "Less Wrong") will have the opportunity and/or interest to apply his/her/its talents to fiction for which they will be paid, as the quality of the writing is certainly eminently publishable.
The new characters are introduced smoothly (Aunt Petunia, while technically the same woman, is about as different from her canon version as Mirror Universe Spock is from the original half-Vulcan, so she counts as a new character). In the introductory chapter, Less Wrong draws on some of the knowledge we only gained much later in the original series in order to set up a completely different meeting of his adoptive family and the wizarding world, in the person of Deputy Headmistress Professor Minerva McGonagall.
The basic concept of the entire fic is (firstly) that Harry is a child prodigy (learning advanced mathematics while in third grade or the equivalent thereof) and thus arrives in the Wizarding World with a firm grasp of the scientific method, logical rigor, and a determination to apply this to figuring out how to best use magic (in a way that none of the prior wizards have).
As a general idea this isn't startling; I'm sure more than half the readers had at least some thoughts of "Jebus, if they can do THAT, why don't they...?" or "if *I* was there, I'd certainly try to...". I'm having to deal with exactly those issues in my current Harry Potter RPG campaign, which includes as PCs or significant NPCs Wednesday Addams, Hermione, Hadji Quest (from Jonny Quest), Jade Chan (from Jackie Chan Adventures) and a number of other ... interesting characters. The basic idea of a "wild card" character from "outside" shaking up an established order is very old, of course.
Old ideas aren't bad in and of themselves, though; the key is whether you can execute them well. And as far as I can see, this is a fic which executes its ideas quite well in many areas. It does, however, have some faults:
I rather liked Harry Potter (V.2.0) at first, but by Chapter 8 I've come to find him extremely annoying. I suspect strongly (and have since chapter... 2 or 3, I think, no later than 4) that Voldemort is actually LIVING inside Harry -- some of Harry's reactions are so very obviously those of an older and badly abused person that I think it's the only reasonable guess I can make. Unfortunately, though we had some nice vulnerabilities and uncertainties at the beginning, Harry's rational approach has been so powerfully effective that we are losing some of the sympathy that we should have just because he's a child being thrown into a world he was not familiar with.
This may well be the effect of the (assumed by me) presence of Voldemort or a part of him inside Harry; Voldy has the reactions of an adult -- if badly damaged emotionally -- man, with of course full knowledge of the Wizarding world, and is thus able through his own knowledge to guide Harry's actions -- but this has the effect of making Harry both much less pleasant as a person, at least in his overt behavior, and also so much more competent than even a prodigy ought to be that he is bordering on Sue-ish competence.
He manages to bully/intimidate/manipulate *McGONAGALL* -- within a day of meeting her -- and ends up calling her by her first name without getting smacked down. This either makes Professor McGonagall vastly weaker as a character, or implies a completely unbelievable force of personality and skill in manipulation on the part of Harry (well, it's believable if you take the assumption that Voldy's doing a lot of the basic work, but that doesn't help in the likeability department).
He then makes friends, or at least allies, with Draco Malfoy, in a sort of Borgia-level manipulation duel which would be perfectly appropriate for, say, Corwin and Eric of Amber or their siblings and relatives, but is very much something else when cast in the context of two children, no matter how well educated.
To Less Wrong's credit, this unlikeable tendency is not unnoticed by all characters; Hermione finds him interesting but extremely annoying as well. The problem is -- as a story -- that if I don't really like spending time with the main character, you need something truly extraordinary in the world to keep me around. Unfortunately, the basic universe of Harry Potter we already know. Moreover, Harry HAS claimed -- in this fic -- the really interesting territory of applying modern thinking to magic, which means that a lot of the good action will be forced to focus around him. I'm not sure I can continue to read the rest if I have to put up with his quite literal decision to Take Over The World (for its own good, of course, not in the way that Sauron meant it -- he wants to merge the two worlds, improve everyone's living conditions and so on) and so far nearly unflappable confidence; even when it SEEMS "flapped", so to speak, he quickly regains his advantages and demonstrates his control of the situation.
The original Harry Potter drew me in because he was a likeable kid trying to find his way in a world that was at once wonderful and an escape, and at the same time frightening and alienating, and we learned about the world with him. This version doesn't have the likeableness or much of the innocence that made Harry fun enough to be around that we tolerated him LATER when he became, for a while, an angsty hard-to-get-along-with teenager and so on. He built up enough credit, so to speak, that we could put up with his later fits of angst, self-importance, or self-pity. Less Wrong doesn't, in my view, give us enough chance for Harry to build up that credit. And he NEEDS it -- especially if my guess is anything close to correct. We need to see the nice boy Harry Potter for quite some number of chapters BEFORE the Dark Influence begins to change him -- otherwise, the real impression is that his niceness was because his mother had influence on him, and now that he's away from his parents he's no longer bothered by the need to be a nice guy unless it gets him somewhere (shades of Tom Riddle). I'm sure that's not the impression the author wants.
Still, it's extremely well written, and many of the ideas are explored well with a good leavening of humor, awareness of pop culture (Harry practically squees in joy when he discovers the existence of what amount to -- and he calls -- Bags of Holding), and carefully worked out logic to the story. I can certainly see why it's gotten so many rave reviews; I just feel it has certain key weaknesses that are probably going to keep me from reading much farther.