Ch. 62-63: I think I found a plot hole. Not as big as the one with eagles in LOTR, but close.
Why didn't anyone ask Harry to drop his occlumency shields and check his memories? There are three people who can propose it:
1) Dumbledore: should have done it immediately upon picking up Harry in Mary's Place, because he still suspected him then. Also the Animagus potion isn't evidence that Harry is innocent, why does everyone think it is?
2) Snape: knows about the existence of the covert message-passing network, knows about the Time-Turners given to students, knows about McGonagall's woefully inadequate method of testing Harry's Time-Turner (just giving Harry a tricky task instead of confiscating the device and checking it), knows Harry had a motive for the crime. A natural first step would be to read the minds of all students with Time-Turners to see if they conveyed suspicious messages on that time/day. He may even stumble upon that accidentally while reading students' minds later.
3) Moody: an order of magnitude smarter and more paranoid than Dumbledore. Should suggest inspecting Harry's memories immediately upon learning the details of the story, e.g. the use of Muggle artifacts in the jailbreak.
Final note: unlike the Time-Turner test, this one can be carried out at any later time unless Harry Obliviates himself or something. It took me three days to get the idea, in-universe characters should be smarter and more motivated than me, so I give them three days of story time and then I will officially declare them stupid.
Even if they don't suspect Harry, they should still have searched his memories in order to figure out what event might have triggered the time-paradox. That really ought to trump any concerns about Harry's mental privacy, and besides, they should expect Harry to go along with it.
Update: Discussion has moved on to a new thread.
After 61 chapters of Harry Potter and the Methods of Rationality and 5 discussion threads with over 500 comments each, HPMOR discussion has graduated from the main page and moved into the Less Wrong discussion section (which seems like a more appropriate location). You can post all of your insights, speculation, and, well, discussion about Eliezer Yudkowsky's Harry Potter fanfic here.
Previous threads are available under the harry_potter tag on the main page (or: one, two, three, four, five); this and future threads will be found under the discussion section tag (since there is a separate tag system for the discussion section). See also the author page for (almost) all things HPMOR, and AdeleneDawner's Author's Notes archive for one thing that the author page is missing.
As a reminder, it's useful to indicate at the start of your comment which chapter you are commenting on. Time passes but your comment stays the same.
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: