Registering some predictions and observations before the next chapter comes out:

Predictions:

The snippet at the start of Chapter 1 is from somewhere in the final chapter. 40%

Lily wasn’t making up the "excuses" Petunia mentioned in Chapter 1; she was indeed warned through some form of Divination that the world would end if she made Petunia pretty, and a centaur did actually tell her not to do so. 95%

Magic’s full power allows the user to rewrite reality. 99% (Look at Harry’s reaction to McGonagall’s Animagus transformation: "Magic isn't enough to do that! You'd have to be a god!" (Chapter 2))

Harry is going to bite someone at Hogwarts who bites him first. 50%

There are indeed "three [items] needed to complete the cycle of infinite wish spells" (Chapter 3) or otherwise ascend to godhood / rewrite reality, and they are the three Deathly Hallows. 75%

McGonagall is unwittingly correct when she says that Harry "triumphed over the Dark Lord by being more awful than he was, and survived the Killing Curse by being more terrible than Death." 60%

Harry will learn how to "cast a Confundus Charm on the entire universe" (Chapter 5). 50%

The "Bafflesnaffle Counter" will be used at some point in the final arc. 50% (Notice that every other item specifically described within the healer’s kit (Chapter 6) has been used at some point so far.)

The surviving Death Eaters will "attack the whole school to get at [Harry]" (Chapter 6). 50%

The fact that Obliviation doesn’t erase all the effects of the experience (Chapter 6) will become plot-relevant in some way, possibly through events that have already occurred (such as the Obliviations performed on Hermione and the Weasley twins). 95%

Sirius Black is not actually imprisoned in Azkaban. 85%

At some point in Harry’s fight against the Dark Lord, "the winner shall lose and the loser shall win" (Chapter 6). 50% (If the Dark Lord is Quirrell, then this may have already happened with Harry learning to lose.)

There will be "Ninety-Five Theses of the Snitchless Reformation" (Chapter 7). 50%

Conditional on there being "Ninety-Five Theses of the Snitchless Reformation" (Chapter 7), those theses will be nailed to a church door. 50%

The customer whom Harry asked about Lucius during the Incident at the Potions Shop (Chapter 7) is Snape. 90%

Harry is "going to tear apart [Draco’s] pathetic little magical remnant of the Dark Ages into pieces smaller than its constituent atoms" (Chapter 7). 98%

Harry will become capable of traveling more than six hours back in time, then return to the train to Hogwarts, making it true that "there are three of [Harry] on this train" (Chapter 8). 20%

The unknown terrible thing that Harry fears during his Sorting (Chapter 10) is that if he fails, Death wins. 80%

Harry will eventually remember his to-do list (Chapter 12). 50%

Hermione’s and Draco’s Christmas wishes will be fulfilled by the House Cup being awarded to Harry, with some acknowledgement of both his Houses. 60%

The note accompanying Harry’s Cloak was written by Dumbledore. 80%

The Remembrall glowing for Harry (Chapter 17) indicates that he’d forgotten something other than not revealing the secret of Time-Turners. 80%

McGonagall will "sit in the Headmaster's office and hear some hilarious tale about Professor Quirrell in which [Harry] and [Harry] alone play[s] a starring role, after which there will be no choice but to fire him" (Chapter 17). 80%

Quirrell will be fired on the last day of the school year. 80%

Snape’s statement that he "can teach you how to ... stopper death" (Chapter 18) will become important. 75%

Harry will eventually investigate Quirrell’s starlight spell. 50%

He-who-is-coming in Trelawney’s aborted prophecy (Chapter 21) is the more resolved Harry after Hermione dies. 90%

Quirrell is an intended hearer (there may be more than one) of Trelawney’s aborted prophecy (Chapter 21). 80%

At some point Draco will show Harry that he’s wrong. 85% (This may refer to the debtor’s meeting.)

Quirrell intentionally gave Harry a paper cut (Chapter 26) in order to forcibly obtain his blood. 90%

Bacon’s diary will teach Harry something about how magic works. 50%

In the prophecy in Chapter 28, at least one instance of "the Dark Lord" refers to Death. 80%

Conditional on "the Dark Lord" referring to Death, Death marking Harry as his equal has something to do with his ability to block the Killing Curse using the True Patronus. 65%

Conditional on "the Dark Lord" referring to Death, the power Death knows not is intelligence and/or rationality. 90%

In the prophecy in Chapter 28, at least one instance of "the Dark Lord" refers to Voldemort. 15%

In the prophecy in Chapter 28, the phrase "the Dark Lord" has multiple referents. 2%

The sense of doom Harry feels around Quirrell is proportional to Quirrell’s strength / health if the distance between Harry and Quirrell is held constant. 75%

No one person can be capable of casting both the True Patronus and the Killing Curse at the same time. 99%

Quirrell wanted to prevent Harry from saving Hermione. 85%

Harry has Transfigured Hermione’s corpse into the ring he wears. 75%

Speculations:

The "moonlight" described in the flash-forward within Chapter 1 could be Patronus light rather than actual moonlight; Patronus light has been described as moonlight repeatedly.

When McGonagall says that she’ll "find a solution [to Harry’s sleeping condition] in time" (Chapter 2), she could have already thought of a Time-Turner as a possible solution.

The nature of Transfiguration might be meant to make readers think about caution and unrecoverable disasters.

Animal Patronuses are easier to cast in the presence of a Dementor because a Dementor’s presence makes most people flinch away from the thought of death and think about something else instead.

The True Patronus is a magically embodied preference for life over death, the opposite of the Killing Curse (which Moody describes as a magically embodied preference for death over life).

Observations:

The 'dark' power of rationality that inhabits Harry is in fact contagious. (Chapter 5)

The Verres family motto, "you can never have enough books" (Chapter 7), is about accumulating knowledge (and hopefully also skills and wisdom). The Potter family motto, "the last enemy that shall be destroyed is death" (Chapter 96), is about defeating death. Harry combines both of these.

Notice what Quirrell says to Hermione: "Knowing things isn't always enough, Miss Granger. If you cannot give and receive violence on the order of stubbing your toe, then you cannot defend yourself and you will not pass Defence. Please rejoin your classmates." (Chapter 16) Even when angry, Hermione doesn’t use any violent or painful spells, and she indeed doesn’t pass Defence. Even with a troll coming after her, she doesn’t try to kill it.

Two things are described as bright red and "blazing like miniature suns": the Remembrall when Harry holds it, and Voldemort’s eyes in Harry’s memory.