Students use a magical telescope during the Astronomy section of the O.W.L. exams.The book has Harry looking for Orion in June at midnight (It's behind the sun in June, so you can't see it even if you wanted to), and also looking for Venus (which being the next planet near the sun is always close to the sun in the sky and therefore never visible at midnight). The students use a magical telescope which when pointed at the ground can see through anything blocking to the stars (the sun excluded) that would be there.
The Veil of Death...
Umbridge is part HagIs Umbridge of Hag heritage - she seems to dislike children and is even violent towards but maybe would shirk from actully eating one though so she may be half or less Hag and this would also explain her hatred of "half-breeds" as she is one herself and keeping it quiet from Fudge and Co.
The Department of Mysteries Level has another name.What's right after the Atrium (eight-rium)? The Mezzanine! (I work security in a building with a mezzanine. I read OOP on shift when it came out and I pass the sign saying "mezzanine" a few times a night and often think this.)
The desk guard at the MoM was dead.Harry notes that no one is manning the desk, but that's all. If they would have looked behind and under the desk they would have seen a body there.
Umbridge was raped by centaurs.Actually pretty plausible: in the Order of the Phoenix Dolores Umbridge is carried off into the woods by centaurs after she insults them. Centaurs are associated with rape in a lot of Greek mythology, to the point where almost every single myth of them involves it. Hermione was probably aware of this, being the Badass Bookworm, but still let her get carried away with no attempt to stop them. When she comes back, we get this lovely bit:
Mark Evans is Harry's (and by extension Dudley's) fairly-distant cousin.Mark Evans and Lily Evans are connected, just so distantly no family member knows. Dudley beat up a cousin of his, and didn't know it. Maybe Petunia (also nee Evans) did know, and chewed Dudley out after Harry had left.