Intriguing bits of information from the book Harry Potter and the Half-Blood Prince

1. New Minister of Magic - Rufus Scrimgeour, almost certainly the Scrimgeour mentioned in OP as asking pointed questions of Tonks and Kingsley about Sirius Black. According to HBP, he was head of the Aurors, so it makes sense.

2. Spelling error in chapter 3? "The misty fug his breath had left on the window..." Should that be 'fog' or not? The word 'fug' is actually an informal British term meaning an airless, smoky, smelly atmosphere. Doesn't seem to fit, really.

3. Definite spelling error in chapter 1, on page 10, end of the 8th line: the word should be 'sight' but it's spelled 'site.'

4. The Rupert thing isn't a spelling error, it's supposed to be a bit of a joke, as if Slughorn can't remember Ron's name.

5. Romances galore:
Ron and Lavender Brown
Ron and Hermione
Ginny and Dean Thomas
Ginny and Harry
Hagrid and Olympe
Lupin and Tonks
Bill and Fleur (cute line: "I am good-looking enough for both of us, I theenk!")
Filch and Pince (now there's a pleasant pair)

6. Deaths galore:
Aragog
Amelia Bones
Emmeline Vance
Hannah Abbott's mom
Florean Fortescue
Gibbon the Death Eater
and then there's that other one

7. Neville's grandmother's name is Augusta Longbottom, and she brags about him in the paper!

8. Contradictory text: Dumbledore becomes Headmaster of Hogwarts ten years after the murder of the Riddles, which would be approximately 1955. That tallies with McGonagall becoming the Transfiguration teacher in 1956, as we are told in OP. However, this passage in PA18 makes no sense:
"Before the Wolfsbane Potion was discovered, however, I became a fully fledged monster once a month. It seemed impossible that I would be able to come to Hogwarts. Other parents weren't likely to want their children exposed to me.
"But then Dumbledore became Headmaster, and he was sympathetic. He said that as long as we took certain precautions, there was no reason I shouldn't come to school...."
Lupin wasn't born until about 1960, so his parents wouldn't be considering ways for him to attend Hogwarts until at least the mid-60s, possible later. It doesn't make sense to say that "then Dumbledore became Headmaster..." when he'd been that for a decade already. Lupin actually starts Hogwarts in approximately 1971.


9. Contradictory text : In Goblet, Harry runs up the marble staircase toward the second floor to go to Dumbledore's office. If he were just going to the top of the stairs, it would be to the first floor, since that's what's at the top of the stairs (the entrance hall and great hall are on the ground floor). In this book, Dumbledore's office entrance is clearly on the seventh floor.

10. Dumbledore's favorite flavor of jam is raspberry

11. The editor of the Daily Prophet is Barnabas Cuffe

12. Who is R.A.B.? My guess: Regulus Black.

13. Why did Dumbledore trust Snape? A bit of speculation -
Did Snape take an Unbreakable Vow saying he'd never betray Dumbledore? If so, who was the Bonder? Aberforth, maybe?

And Snape, after more or less being tricked into vowing to kill Dumbledore, went to the Headmaster and explained the predicament he was in. One of the two of them had to die, and Dumbledore quickly realized it would make more sense for it to be him than Snape. So they planned for Dumbledore to spend the year getting Harry up to speed while Snape kept Draco under control, then Snape killed Dumbledore. At the last moment, Snape almost couldn't do it and Dumbledore had to tell him "Severus, please..." Now Snape has proven beyond a shadow of a doubt that he is Voldemort's best and most wonderful supporter, and is therefore in the best possible position to help the side of good.