Three shall be Peverell's sons and three their devices by which Death shall be defeated.

• chapter 96

The one with the power to vanquish the Dark Lord approaches, born to those who have thrice defied him, born as the seventh month -

• chapter 86

There has previously been some speculation that the dark lord in Harry's birth prophesy is death rather than Voldemort. I think this interpretation just got a lot stronger.

James and Lilly had defied Voldemort but not death. The new lines back an interpretation that the Peverells thrice defied death with the three deathly hollows and Harry is born to the Peverell line.

This is, in some ways, a more natural interpretation of that clause since James and Lilly were in the Order and were defying Voldemort on a daily basis not just 3 times. The line of the Peverells makes the number three make sense rather than being arbitrary.

Just spelling out that we have a much better idea now what the first lines of the book mean:

Beneath the moonlight glints a tiny fragment of silver, a fraction of a line...

(black robes, falling)

...blood spills out in litres, and someone screams a word.

The silver likely refers to:

Neither of them noticed the tall stone worn as though from a thousand years of age, upon it a line within a circle within a triangle glowing ever so faintly silver, like the light which had shone from Harry's wand, invisible at that distance beneath the still-bright Sun.

There'd been some discussion of why HPMOR!Hogwarts was founded around 1200, as opposed to canon Hogwarts, which was "established around the 9th or 10th century." This chapter seems to make the reason clear: the founders were near-contemporaries of the Peverells, who kept their canon birthdates. Godric Gryffindor in particular seems likely to have been involved.

silently, making less noise than the dead leaves slithering along the pavement...

This is a quote from canon, in a scene where Harry is nearly possessed by Voldemort; it's Voldemort's memories of the night he died. It's italicized, as with Harry internal conversations, suggesting that this is part of Voldemort in Harry, remembering the night he died. (?)

It strikes me that this is even more obviously a turning point than it already is.

First: This is the first hint to Harry that he is not alone. All this story, Harry has been defined by his aloofness; the one person as "sane" as he is cannot be trusted, and for all that Hermione tries she's just more of a apprentice than a co-hero, she's not on the same scale that Harry acts on.

No longer. Harry knows, now, that there are more like him, and they too are smart, and competent, and they have gifts for him from hundreds of years in the past.

Second: This also solves one of the problems I had been worrying about, which was: How can Harry solve Death without it looking like a Deus ex Machina? Sanderson's First Law: magic cannot be used to solve a problem except where it is foreshadowed and constructed from existing effects. There's been a few ideas tossed around - Summon Death + True Patronus and the like - but they all seem to have... unhelpful side effects. (In particular, actually ending "Death" would be a bad thing, because Death kills bacteria as much as it kills humans. You want to destroy "Death of Humans" or come up with a mass-producible immortality elixir, not kill Death outright.)

For those who don't know, the actual origin of "The last enemy that shall be destroyed is death" is Corinthians 15:26, specifically, the King James version.