I have been reading many of the FFs here based around Harry Potter and that universe - that will be obvious by my favourites. Since reading FFs, I have seen and thought of many little niggles and will list them here as I see them and think of them: they will be in no particular order...
Love Potions - are they ok or not? Molly Weasley has Ginny and Hermione giggling about her experiences with them, Ron is slipped one meant for Harry and they learn to make them in Potions class. However, can any high schooler (or, for we UK types, anyone taking GCSEs) remember learning how to make Rohypnol in chemistry class? And, since they do affect the emotions and mind, why were there no comebacks from the school when Ron received one?
Pop Culture - where is it? Aside from one or two mentions of the Weird Sisters and Celestina Warbeck, no one discusses pop/rock/whatever music, no one mentions films or books or art. The Muggleborns and Half Bloods don't have comedy catchphrases culled from the television and no one talks sport. To be honest, the kids at Hogwarts are dull as dishwater.
Propaganda - why did Albus Dumbledore not release a "tell all" about Tom Riddle/Voldemort in any of the years since his first rise? Tom had Rita Skeeter do a complete hatchet job on Dumbledore after his death, so why didn't anyone at all try to do it to Voldemort - especially when they thought he was dead?
Love Interests - the main canon ships are crap. Constant bickering does not mean sexual tension. Unless you're nine years old. It means deep seated problems. And who would see "she looks like my dead mother" as a good reason to start dating and fall in love with someone. That says "oedipal interests". Ginny, as described in canon, is a fling at best.
Dumbledore - there has been much written here about Dumbledore. I hated him in canon - how come no one spotted that he practically runs the British Wizarding World? Chief Warlock (heads up the Judiciary), Supreme Mugwump (very senior role in the Wizarding UN) and headmaster of seemingly the only school in the UK (gets to mould young minds early). He is essentially a dictator; why else would everyone be so deferential - no other headmaster is allowed to interfere with their students' lives like he does. He is too easy to turn into a villain just by following canon.
Note added 3/11/2013
I just had an idea for a crossover I have never seen before: an HP/Zoolander fic set after the film. Harry is raised by Derek Zoolander and Matilda and his wacky uncles Hansel and Maurie. "The Power He Knows Not" would be the "Magnum" look (or similar). First year would set the stage for this very very very very good looking 11 year old to fit into Hogwarts - he would give grooming tips to Draco Malfoy and Snape, fix Hermione's look (in the same way Zoolander did in the film) and destroy Voldemort with the "look". 2nd year he would focus on mocking Lockhart's grooming advice and point out how badly photographs are affected by all the charms he has on him. Not sure where it could go from there though. A hand mirror to blind the dragon in 4th year maybe?
If anyone does fancy tackling it, feel free.
Note added 24/11/2013
Just saw this on Youtube: Mitchell & Webb's sketch "Welcome to Hufflepuff"
Note added 09/07/2014
Damn it. I'm now into Naruto fan fics (despite never having seen or read the Anime or Manga) and am a NaruHina and NaruIno shipper. And on top of that, I've been sucked into the Buffy and Angelverses. With a focus on Xander as main character since he was the one who didn't get any significant power ups throughout the series and still managed to be awesome. I think Whedon went overboard on the whole "girl power" schtick. Still excellent and fun series though. And I ship XanderFaith, XanderCordelia, XanderDawn and XanderDrusilla. I may need help.
Note added 15/08/2015
Speaking of the Buffy and Angel series: just who exactly is Angel?
Essentially we have 3 personas: Liam, Angel's original human identity; Angelus, the evil vampire created from Liam; and Angel, the being created when Angelus got his soul restored. The 3 personae are very different: Liam was a young Irish man who had fairly wealthy parents, didn't need to work and enjoyed drinking and sleeping around and getting into fights. Angelus the vampire is supposedly Liam without limits: thoroughly evil but very charismatic. Angel is Angelus with Liam's soul restored to him and therefore should be the same as Liam plus vampire strength and speed, immortality, the need for blood and a few pointed (and fanged, ho ho) life lessons- essentially, Angelus-lite.
Anyone who has seen the series knows that Angel likes classical, operatic and Barry Manilow music, fine wine and enjoys reading Gothic romance and horror. So nothing like Liam at all. Therefore, either the idiot gypsies ripped the wrong soul from heaven to torment Angelus or Joss Whedon had a massive chubby for a sophisticated elegant adult vampire banging a teenage girl. I wonder which one it could be?