Stealth - not only he must transfer cloak to Hermione - he must also get Hermione out of court, and she must be in cloak at all times to prevent tracking magic, and Harry must have the cloak with himself, when Dumbledore will want to see it, when tracking magic will stop working (and there's spell that detects if cloak is nearby).
One way to do this - duplicate cloak using time turner for the moment Dumbledore will want to check it.
Scheme:
Harry takes cloak, mokesking pouch, and time turner with himself to the court
Harry waits for Hermione to disappear
Harry puts his mokeskin poach under the table or somewhere and not look at it
Hermione disappears
Dumbledore try to track Hermione and fails - so he checks if cloak is near - it is, so he asks Harry about it - Harry shows cloak to Dumbledore and it's empty
Harry goes back wearing cloak just before the moment Hemrione should disappear, takes the mokeskin poach that he left under the table, somehow makes everybody look elsewhere and put Hermione into his own mokeskin poach which he keeps under the duplicated cloak (may need to use potion or sth that will turn Hermione into animal or thing or sth that he can put into poach - like with Quirrell as a snake).
Harry in the past waits for Dumbledore to check the cloak that Harry in the present has with himself, waits for everybody to get out, and somehow passes the poach back to himself without looking at himself. Harry in the present puts poach into the cloak.
Possible failures - Dumbledore can keep the cloak, making it impossible to hide Hermione after the time turner is used up. I think Dumbledore won't do this - he didn't wanted to keep cloak to himself, he wants Harry to have cloak just in case, and even if he see throught this plot, he can let it slip, because he probably don't want Hermione to have wand snapped. But it's one failure mode.
Also Harry must be prepared to "prove" he didn't used up his TimeTurner, like he did after Azkaban Breaking.
I probbly missed something, and this won't work.
How would Harry even get to the trial in the first place? Dumbledore won't let him leave Hogwarts, and if he did, why should the Wizengamot admit him to the proceedings unless e.g. Dumbledore requested it? And why would D. do that unless he expected Harry to succeed in helping Hermione escape? But if D. wanted Hermione to escape illegally (possible but unlikely IMO), he could surely arrange that himself without Harry's help and presence. (Maybe he'd borrow the cloak...)
(The HPMOR discussion thread after this one is here.)
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. There haven't been any chapters recently, but it looks like there are a bunch in the pipeline and the old thread is nearing 700 comments. The latest chapter as of 7th March 2012 is Ch. 77.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes.
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, nine.
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: