The chapter called "Snape's Worst Memory" is entirely accurate, but not for reasons you'd initially expect. After reading Deathly Hallows, you may realize that it's not his worst memory because he was bullied beyond humiliation by James and Sirius (in fact, it's implied that said bullying was a regular occurrence- though also that James and Snape were sworn enemies and therefore always at each others' throats), but because in his rage, he called Lily (who he was in love with) a Mudblood, which totally and completely destroyed his chances of getting together with her.
It may seem odd that Umbridge is so indulgent to the Slytherins right from the start as compared to every one else. But then you realize that her entire life is based around petty ambition. Ambition is the defining trait of Slytherin House; she would have been a Slytherin in school.
Not to mention that while this book doesn't tell us that she shares the "pure wizarding blood" obsession characteristic of most pure-blood Slytherins, her contempt for part-humans is a rather nasty likeness. And based on the last book she may indeed have had contempt for "Mudbloods," though YMMV - her enthusiasm might have simply been because of her desire for power in "the Establishment" regardless of what form "the Establishment" takes, or even just out of pure nonspecific sadism.
After Harry's actions accidentally lead to Sirius's death, Dumbledore tells Harry that he knows how Harry feels. In Deathly Hallows, we find out that Dumbledore also accidentally got someone he loved killed.
"I am not aware that it is any of your business what goes on in my house—"
"I expect what you're not aware of would fill several books, [Vernon] Dursley," growled Moody.
Just think about Moody's wording for a second. Then laugh to yourself and wonder if it was intentional.
The students who used the snackboxes claimed they had "Umbridgeitis". In other words, Umbridge was making them sick! Or they were sick of Umbridge, either way. . .
Fudge asks "Squibs can't see Dementors, can they?" File that right in there with Wizards being clueless about Muggles - despite the fact that they are at the ministry they don't even seem to have a "Department of Squibs" who can answer that question immediately.
Change it to them sleeping and snoring in a comically loud fashion? The other half of this is that unlike Harry and co, Molly wasn't attempting to get rid of the boggart in a safe, classroom environment. She's in a big creepy house and is doubtless on edge already (she even says so herself after Lupin gets rid of the boggart). There's a theory I've seen floating around that boggarts don't necessarily take your very worst fear, just whatever is currently lurking closest to your consciousness. Granted, in Molly's case, it's probably both of those at the same time, her greatest fear and something that's been on her mind lately.
You don't realize it until Half-Blood Prince, but the nonverbal spell Snape uses on James during the flashback to cause a gash to appear on his cheek is likely Sectumsempra. The spell that, if cast correctly, causes deep, painful and profusely-bleeding blade wounds, irreparable severing of body parts and is overall very tricky to use in any way that DOESN'T kill your target if you get a clear shot. He was aiming that at James' head. One mistake on his part or a slower reaction time on James' could have resulted in the later getting decapitated right there. True, James' bullying was certainly despicable, but still, you know, MURDER. Snape was being the guy who smuggles a .45 to school and pulls it out during a schoolyard brawl, and we're supposed to sympathize with him?
The incident from the flashback happened in Snape's fifth year at Hogwarts, while Sectumsempra was written in his 6th year Potions textbook. None of the descriptions of James Potter as an adult mention him having a nasty cheek scar, which that spell would surely have left. So isn't it more likely that Snape used a weaker spell at the time, that inflicted lesser wounds, and later developed a stronger version "for enemies" once he'd seen how easily the infirmary undid the damage James had suffered?
Dolores Umbridge's eventual comeuppance. She is abducted by the centaurs after Harry and Hermione lead her into the Forbidden Forest. Anyone who knows the mythology of centaurs knows that they RAPE human women. This totally explains her mood when she is in the infirmary later on in what can only be described as a traumatized state. It also lets you know that you should never fuck with Hermione or her friends, as it was HER idea.
Minor Fridge Horror compared to those above, but: Nobody in the wizarding world receives much education about mundane matters, basic human physiology included. Fred and George repeatedly tested their Skiving Snackbox treats, both on one another and on ill-informed volunteers. We know there was at least one accident with Katie's unstoppable nosebleed; how easily might the twins have put themselves or others in the infirmary, or even St. Mungo's critical-care ward, if they kept making people bleed, puke, or suffer fevers in complete ignorance of the very real dangers of anemia, dehydration or hyperthermia?
Presumably the twins don't want to kill off their potential customers. It's likely that the symptoms their snacks create are purely cosmetic effects; bleeding or barfing, for example, might actually conjure up what's expelled rather than taking it from the user's own body.
Sirius gave Harry a magic mirror as he left for Hogwarts, which Harry chose not to open and forgot about. Poor Sirius, cooped up alone at Grimmauld Place, probably wondering if Harry was ignoring him.
It took the DA several hours to fly to London — why didn't Snape 'n' pals get there earlier?
It took longer. Harry's takeoff time is at sunset; when Dumbledore portkeys Harry back to his office, dawn is breaking. The kids must have been in the air all night and well into the early AM. Now has a Headscratchers entry.
Harry and co were riding on the Thestrals - who have an amazing sense of direction. It took some time for Snape to find out that Harry and Hermione had gone into the forest. He would have had to hunt them down, probably question a few centaurs (and that can't have been easy) and contact all the Order members, including Dumbledore. That's probably an extra hour onto Harry and co at least. And they probably had to run around the Ministry for a good bit before they found everyone. Remember they probably went to the Hall of Prophecy first and had to run around looking for the right room.
Why is there no-one guarding the Ministry of Magic overnight?
Fridge Brilliance: They need Harry and co to get to the Hall of Prophecy so he can take the prophecy off the shelf personally. They deliberately took out all the employees so Harry would have a free path to the room. They were probably following them around the whole time (Disillusionment Charms perhaps?).