Warning: Unmarked spoilers on this page.
You may put examples from both the book and film adapations.
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The Polyjuice Potion can give you the appearance of anyone you can get a sample of hair from- not just a clever disguise, but it alters your body so you have the same fingerprints, hair, and body shape. Thus anyone important can be replaced. You'd Expect: The potion to be illegal for use by anyone but Aurors and high-ranking Ministry officials. Instead: Although the Polyjuice Potion is considered very advanced magic, it is not only legal, the recipe and the ingredients can be acquired in the school library and the closet of the Potions class respectively. Also, an (albeit very bright) second year student is capable of brewing the stuff. Also even within the Ministry there is no form of regular polyjuice/identity check.
And that's not even getting into Hermione's little accident where she mistakes a cat hair for a human hair. How the Hell can the smartest witch of her generation, or even just a person of average intelligence, possibly mistake a cat hair - or any animal hair for that matter - for human hair? It's just barely possible if the person in question wears their hair in a crew-cut (gross hair length won't give it away then, and thickness and texture are subtle details that can be overlooked), but Millie is a teenaged girl; if she were wearing her hair in a buzz cut it would have been noticed and remarked upon.
It turns out that there's a way to dispel the Polyjuice transformation - a magical waterfall that washes the false appearance away. You'd Expect: That such crucial institutions as the Ministry of Magic and Gringotts bank would install such wards right at the entrances. Instead: The Ministry of Magic doesn't have it at all. Gringotts does, but only deep inside the building. As a result, the heroes are able to infiltrate both places using Polyjuice Potion. Maybe the Ministry can be cut some slack as we don't know if Gringotts would share its knowledge with them, but Gringotts itself is still getting nowhere near as much mileage out of their security systems as they otherwise could.
From the second book onwards the same situation repeats itself: some crucial events take place with either no witnesses or kids (usually Harry) as witnesses, and afterwards nobody believes them. You'd Expect: They would use the Time Turners to send back an invisible observer and oversee the events in question. Instead: They never do, and it constantly gets worse.
Speaking of which, Time Turners, potentially the most powerful and destructive artifacts in the world are kept in the Ministry of Magic. You'd Expect: Them to be kept in the most secure, out-of-reach place, accessable only to the select few. Instead: They are kept on an open shelf, with no guards or wards, accessable to a bunch of kids. As a result, they immediately get destroyed, once the Trio even gets near.
Despite having Horcruxes, Voldemort is still horribly crippled after being hit by his own Avada Kedavra as he tries to murder Harry. In order to regain his power, he needs someone to perform a ritual involving bone of his father, flesh of his servant and blood of his enemy. Harry knows all of this and so does Dumbledore. You'd Expect: The heroes to try and take out Voldemort, ignoring the Horcruxes until he's dealt with. Sure, it's almost impossible, but Harry was lucky to even have a shot at this guy during the Battle of Hogwarts. While Harry and his companions are above killing people, Dumbledore could do it and after learning about Voldemort's immortality he was dying anyway, so why not try yourself against the guy who's slightly weaker than you, when you have nothing to lose? Of course, Voldemort wouldn't die, but he'd be out of the picture at least. The Death Eaters wouldn't last without him. Instead: They hunt the Horcruxes first, with no plan to kill Voldemort and defeat his army after finding and destroying them.
Dumbledore is revealed to be a highly skilled Legilimens in the fifth book of the series. You'd Expect: Dumbledore to try using this skill for something, such as finding out who opened the Chamber of Secrets both times in the series. Granted, this might not work, and could be a VERY controversial step, with the students and their parents getting very upset about Dumbledore's mind-reading, but Dumbledore could point out that with someone going around petrifying other students, he's got a very good excuse to take such measures. Instead: Dumbledore's Legilimency is only used in the fifth book, to find out why some of the events of the climax happened.
Dumbledore is aware that someone is attempting to steal the Philosopher's/Sorcerer's Stone, that they were good enough to make a serious attempt to steal it from Gringott's, and there's a strong possibility that it involves Voldemort. You'd Expect: Him to recruit former members of the Order to protect it, to surround it with spells that only let the right person past them and to keep its location a secret from everyone outside of that very small group of people. Hell, a Fidelius Charm would be enough, and Dumbledore has an extremely skilled Charms user on his payroll. Instead: He relies on less than competent people like Hagrid to supply guards and didn't quiz Hagrid on potential problems for those guards. Worst of all, his security used obstacles that were really less security and more puzzles. Admittedly they were tricky but first year students were able to get past the same puzzles that were intended to stop a dark wizard controlled by Voldemort. If not for the last spell cast on the mirror you would have to wonder if Dumbledore was unconsciously trying to let Voldemort return to life.
There's also the very decision to house it at Hogwarts, a school full of the next generation of magic users. Sure, it's one of the most well-protected places in the Wizarding World, but it is also intentionally placing the students in danger of getting caught in the crossfire, combined with the natural tendency of kids to go specifically where they are told not to, which is exactly what Dumbledore says at the start of the year: "Stay away from the third-floor corridor."
The Stone's final defense was probably the worst part. Dumbledore thought that it would be brilliant to make the Mirror of Erised just hand over the Stone to the intruder if they weren't planning to use it. Granted, they'd probably need a way to get the Stone out of the mirror, so that the Stone's owner can keep making the Elixir of Life, but why give it away like that? No reason was given. But no worries, the thief must automatically have good intentions if they don't intend to use it, right? And it's not like they could just use someone who didn't plan to use the Stone to get it, just like Quirrell and Voldy did.
Voldemort, while possessing the body of Professor Quirrell, wants to kill Harry Potter without openly revealing himself so he can remain on-campus to steal the Philosopher's Stone.
You'd Expect: That since he enjoys every possible advantage in this situation (Harry does not yet know he is a bad guy, Quirrell is one of Harry's teachers and in a position of authority over him, he is a fully trained wizard and Harry is an 11-year-old boy who is only beginning to learn elementary first-year spells), he would find it trivially easy to arrange to catch Harry somewhere alone and without witnesses and then murder him in any one of a myriad of possible ways that would plausibly look like an accident, or frame someone else for Harry's murder. Particularly: If he stunned Harry, then threw him into the room with Fluffy the Cerberus and let him get eaten, which would accomplish multiple objectives at the same time — it would kill Harry while making his death entirely look like "death by misadventure", it would politically disgrace Dumbledore that the Boy-Who-Lived died on Hogwarts grounds from a security measure set up by the school authorities, and it would force either Dumbledore or the Ministry of Magic to order the Cerberus removed from the school as a deadly hazard to students and thus remove the principal obstacle standing between Quirrellmort and the Philosopher's Stone. Instead: He tries to kill Harry by jinxing his broom during a Quidditch match, which means his murder attempt is done in broad daylight, in front of hundreds of spectators, and in such a manner that Harry is literally not yet back on the ground before every observer with the IQ of a houseplant has figured out that someone is attempting to kill Harry Potter.
Chamber of Secrets
Harry and Ron for some reason cannot pass the magical barrier leading to the Platform 9 3/4, but all the other Weasleys are already there, the train has already left, and the boys are afraid that Ron's parents might leave the station another way. Harry suggests that they return to the car they arrived by, because people are starting to stare at them. You'd Think: That the boys would just go to the car and wait for Mr and Mrs Weasley to get back, since they obviously wouldn't abandon their car. Or, failing that, they could take Professor McGonagall's suggestion after the fact and just send an owl. Instead: Ron gets a "brilliant" idea to steal the car and drive it to Hogwarts. Car's stealth mode malfunctions, it gets seen by non-wizards, kids get detention, Arthur is fixed with a huge fine, and the Weasleys lose the car.
Voldemort gives a Horcrux, his old school diary, to Lucius Malfoy, as part of his plan to reopen the Chamber of Secrets, but since he's incapable of trusting anyone, he doesn't tell Lucius what it is, just that it's a powerful magical artifact. You'd Think: He would tell Lucius that he values the diary's safety more than he does Lucius', and that if Lucius does anything without Voldemort's express orders, death itself will not be enough to save Lucius from very slow, very painful retribution. Hell, Voldy could suggest that the diary has powerful wards on it that will be activated if Lucius uses it without permission, so that Lucius would hesitate to use it in a cavalier fashion even if he was 100% convinced Voldy was dead. Instead: Voldy does none of this, apparently confident that Lucius would never take any initiative whatsoever regarding Voldy's stuff. So Lucius decides to carry out the plan anyway for his own ends, and gets a portion of his master's soul destroyed.
Throughout the year, muggleborn students, along with Filch's cat, suffer attacks from an unknown assailant that leave them petrified. Right after the first attack, it is established that a potion known as Mandrake Draught can cure the victims. You'd Expect: The school to try and buy some of this Draught from an outside source as soon as possible, so that the students can be treated quickly. Granted, the person responsible for the attacks might have destroyed or contaminated all the Mandrake Draught in the country earlier to prevent the school doing this, but we see no evidence to suggest this happened, and in any case, the idea of one person being capable of this seems a bit far-fetched. Instead: The school decides to make the Draught itself, even going so far as to grow its own Mandrakes. The problem is that the Mandrakes take most of the school year to mature, and therefore become usable. The result is that the assailant's victims miss out on a substantial part of their education for that year.
The diary mentioned earlier ends up in the hands of Ginny Weasley, who eventually suspects that it's connected to the attacks on other students. And she's right: It's possessing her and having her set a basilisk on people. She tries to get rid of the diary by flushing it down a toilet, but later discovers that it's in the hands of Harry Potter. Not wanting him to discover her crimes, she steals the diary back. That's understandable, but her next actions really take the biscuit. You'd Expect: Ginny to try and dispose of the diary a bit more thoroughly than she did last time. Instead: She writes in it again, and as a result, the diary has her attack two more people and Ginny herself almost dies. Granted, she probably wanted to confirm how much the diary had told Harry, but it was still a bad idea.
Harry and Ron have figured out that the monster in the titular chamber is a Basilisk. Shortly after overhearing that Ginny has been taken to the Chamber, and then witnessing the teachers telling Professor Lockhart to deal with the monster, they decide to give him this information. When they do so, they learn that Lockhart, who has supposedly dealt with all manner of dark creatures in the past, is in fact a fraud who takes credit for deeds other wizards and witches have done. You'd Expect: That, since Lockhart has proven himself to be incompetent at this sort of thing, Harry and Ron would seek out the other teachers and get them to deal with the Basilisk. Instead: They decide to bring Lockhart along anyway. While in the Chamber, Lockhart attempts to abandon Ginny and completely wipe both Harry and Ron's minds in order to stop them revealing his secrets. They only avoid this due to Lockhart using Ron's broken wand, causing the spell to backfire on him. Even if he hadn't tried this, there was virtually nothing he could have done to help the group.
Prisoner of Azkaban
In the backstory Harry's parents are warned that they've been targeted by the Big Bad and need to hide. They choose a spell that perfectly conceals one's domain, as long as a chosen person (the Secret Keeper), well, keeps the secret. You'd Expect: They would become Secret Keepers themselves. Deathly Hallows explicitly shows this is possible since during that book, Bill and Arthur Weasley are able to be the Secret Keepers for their respective dwellings. Furthermore, Dumbledore was Secret Keeper for #10 Grimmauld Place in Order of the Phoenix, a place that he was then able to visit and stay in freely. Instead: In gross violation of the Evil Overlord List #222 they make another person the Keeper, and it fails. Granted, that person betrays them, but even without that their plan wasn't as foolproof as it could have been.
James Potter's first choice for his Secret Keeper is his best friend Sirius Black, despite the fear that someone close to the Potters is working for Voldemort. Fortunately for him, Sirius isn't that someone. You'd Expect: That if Sirius was prepared to die to protect the Potters, he'd accept the Secret Keeper position, and go into hiding so that Voldemort coundn't find him. After all, if you want something done right, sometimes it's better to do it yourself. Also, it would be a good idea to keep a wizarding equivalent to a cyanide pill on him at all times, in case Voldemort does track him down. Or Better Yet: The Potters would make their Secret Keeper someone they trust absolutely (duh), someone who Voldemort was already 100% determined to murder as priority one (so that being the Secret-Keeper doesn't put them in any danger that they weren't in already), someone who is a Master Occlumens (so that Voldemort, a known Legilimens, cannot read their mind), and someone who can straight-up kick Voldemort's ass any day of the week and twice on Sundays (so that Tom can't get it out of them by main force). In other words, that they'd use Dumbledore. Who had already volunteered for the job. Instead: Sirius convinces the Potters to make their other friend Peter Pettigrew the Secret Keeper, his logic being that Voldemort would never think of going after someone like Peter. This is despite the possible traitor within his group of friends. Peter turns out to be the traitor, sells the Potters out, and later frames Sirius for their deaths. And that's not going into the fact that, if Voldemort does go after him, he could easily interrogate Sirius on who the real Secret Keeper was.
Dumbledore accepts a kid into his school who's a werewolf and once a month turns into a monster with a love of human flesh for several hours. To get round this problem, Dumbledore decides to build/designate a location near the school where the kid can safely transform. You'd Expect: That when the full moon approaches, they would escort the kid there under an invisibility cloak or disillusionment charm, or anything similar. Instead: They bring the kid there without any concealment every time, from what we see. As a result, another kid ends up seeing him being taken there, and his curiosity nearly gets himself killed. You'd Also Expect: Whoever's in charge of the kid not to let him know how to get past whatever's in place to stop other students coming across him. Instead: They don't, and as a result, the protection eventually fails and nearly leads to the death of another student.
Years later Dumbledore employs the same werewolf as a teacher. This time, however, they have a remedy that allows him to retain his sanity while transformed, so he can just wait through "those times of the month" in his office. The remedy must be taken regularly for several days following to the full moon. You'd Expect: That they'd provide for some reminders and a contingency protocol, like a lockdown on his office when the "zero hour" approaches. It's not some flu medicine he's taking - it's supposed to keep him from going rabidly insane in a castle full of children. Instead: Nothing of that kind is done; on one occasion he neglects to take the potion and nearly kills several students.
Sirius Black, an innocent man believed to be responsible for the death of Harry's parents, wants to kill Peter Pettigrew, the Traitor who was responsible (who conveniently turned himself into a rat 12 years ago and is still in disguise as Ron's pet) and prove to Harry he's innocent. You'd Expect: Sirius would try and get in contact with Dumbledore shortly after he escaped from Azkaban, and explain the truth to him. That way, Pettigrew can be taken into custody, keeping Harry safe, and Sirius would be cleared of all wrongdoing. Instead: While trying to capture Pettigrew, he violently attacks the Fat Lady's portrait, and later enters Gryffindor Tower with a knife drawn. These actions get him no closer to finding Pettigrew, and actually incriminate him further. Later on, he turns himself into a dog, grabs Ron and Pettigrew, drags them into a secret shack, and waits for Harry to follow You'd Expect: That first chance Sirius got he would cast the spell to return Pettigrew to human form and explain to Harry what happened. Instead: He just leaves Pettigrew in rat form. When Harry arrives it looks like a trap, and Sirius says things like "Only one will die tonight" which just confirms to Harry that Sirius wants him dead, making Harry try to kill Sirius.
A murderer and traitor has been captured by the trio and two adults, and they need to escort him to the castle. They know full well that he's an Animagus who can turn himself into a rat. You'd Expect: They'd use a simple Stunning Spell on him then float him to the castle, like they're doing to Snapeat the exact same time. Or summon/conjure a jar, put him in it and make it unbreakable so he can't transform just like Hermione does with Rita Skeeter's bug form in the fourth book. Instead: They leave the murderer awake and chain him to two of them, one of who is about to turn into a werewolf. As soon as he does, the murderer transforms and falls out of his chains, leaving Ron chained to a hungry werewolf. But just before that happens... You'd Expect: Hermione, or Sirius, who's currently carrying Snape's wand, to Stun Lupin, or magically restrain him in some other way as he's in mid-transformation (e.g. Hermione's full-body-bind curse). Instead:Siriusshapeshifts into his dog form in order to fight Lupin off. He succeeds, but ends up in a great deal of pain, and nearly has And I Must Scream invoked on him by Dementors as a result.
We learn in this book that the Wizard World has Time Turners, devices which can be used to actually travel back in time. Admittedly they are limited in how far back they can go but even a short distance would allow someone to get access to a huge amount of secret information or, if they were careful, actually interfere in the past. You'd Expect: The devices to be kept under the strictest guard possible, for knowledge of them to be suppressed as much as possible and for them to only be used at times of the greatest need. Instead: One was given to a child so she could attend more classes. While Hermione is more competent than most adults we see they still ran a horrible risk the moment they made it available to her, if only because someone might have realized she had one and stolen it.
Goblet of Fire
Despite Harry not applying for participation in the Triwizard Tournament, his name still comes up. The only explanation they have is that someone tampered with the Goblet of Fire, the device that selects participants, and planted the kid into the Tournament. However, when it is quite reasonably suggested that Harry should be excluded, the answer is that it's impossible, because when Harry's name came out from the Goblet, he was entered into a magical contract and has to participate (yep, without his knowledge or consent). You'd Expect: That someone, anyone would then enquire what exactly that contract stipulates, what are the consequences of violation, are there any escape clauses or loopholes, how exactly does it define "participate" and what happens if Harry just sits the contests out and so on. Mind you, there are a lot of people who are unhappy with this development, starting from Harry himself and then to his friends and the supporters of the legitimate Hogwarts champion and the delegations of the competing schools. Granted, it's possible that there's no way around the goblet's decision, but it never hurts to cover all the bases. You'd Also Expect: That the adults would try to find out the culprit. After all, Moody admitted that it took a very powerful wizard to tamper with the Goblet, and those could be counted on one hand. Hell, cliched is it may sound, all the possible culprits were literally in that very room where they were discussing the situation. Instead: Nobody does anything, and the fact that Harry's participation was orchestrated is completely ignored. There's no investigation, and even when the final task comes, so whatever the culprit's intention was this is their last chance to act upon it, no one is keeping an eye on the participants, and the villain has the free reign to rather blatantly interfere with the task and ensure the completion of his evil plan. Moreover:The second and third tasks are a rather baffling moment for the entire school, because even setting aside the suspicious circumstances surrounding Harry's participation, somehow none of the hundreds of people present saw it as odd that during the grand events of the Tournament nobody gets to see the contestants.
Hermione first learns of the Hogwarts house elves during this book. She isn't happy when she finds out that the elves work without pay, sick leave or pensions, and decides to set up the Society for the Promotion of Elfish Welfare (S.P.E.W.) to try and improve things for them. You'd Expect: That if Hermione was serious about fighting for elf rights, she'd look for cases of elves who had genuinely suffered abuse and mistreatment from their masters and/or the ministry (e.g. Dobby, Hokey, the elves of the Black family, etc) and base her arguments around them. You'd Also Expect: That she would chose a name for her crusade that doesn't sound so stupid and utterly impossible to respect. Instead: She only uses the Hogwarts house elves as an example of why elves need rights. Elves who, despite not being paid for their work, are quite happy with their lot in life. As a result, no-one takes her case seriously.
Barty Crouch Jr. is using Polyjuice Potion to take the shape of Mad-Eye Moody, this year's DADA teacher. In order to maintain his disguise he needs to drink a fresh dose every hour. You'd Think: Since he already knows how long he has to stay at Hogwarts and can do basic arithmetic, he'd come prepared with all the doses he needs for the year squirreled away in his bottomless trunk or somewhere else. Or At Least: If he needs a mid-year resupply, he'd simply contact one of his co-conspirators (such as Wormtail) outside the school and have them nip down to Knockturn Alley and buy him some. Instead: He steals the ingredients necessary to brew a fresh batch from Snape's inventory of ingredient storage, despite the fact that this would be very likely to advertise to anyone who finds out that somebody is making Polyjuice Potion. The only thing that saves Crouch from having to duck a school-wide manhunt is Snape blaming Harry Potter for the theft because of both his hatred for the kid, and the fact that some of Harry's possessions ended up near the scene of the crime.
Over the course of the first three years, the campus has twice been menaced by a person possessed by the spirit of Lord Voldemort, and by a hidden Death Eater animagus and an Azkaban escapee. All of these individuals were able to freely move around the campus, make multiple murder attempts on-site, and abduct or lure Harry Potter into an isolated location. You'd Expect: Dumbledore to start showing some awareness that Hogwarts is likely to be threatened by people who are not who they appear to be, and also that the campus needs tighter precautions against people sneaking in and tampering with things. Instead: A shapeshifting impostor taking the guise of one of Dumbledore's oldest friends literally sits next to him every day at dinner for ten months, and Dumbledore doesn't notice a thing (which is particularly horrid given that Dumbledore can read minds, and even if he's not suspecting shapeshifters after Quirrell and Ginny Weasley he should at least be taking slightly more precautions against possessed people), and continues to not suspect anything even after a series of odd events has occurred that this 'old friend' is always lurking around the periphery of in one role or another. As Well As: Having the sum total of the physical security on the Goblet of Fire be an Age Line, which would only stop the students and do absolutely nothing to prevent any adult wizard — such as, oh, all the Death Eaters still out there wanting to kill Harry Potter — from tampering with the highly important magical artifact the highly hazardous tournament centers around. Despite over half a dozen on-campus murder attempts over the past three years the maximum level of security used is intended against attempted student pranks only, and is never increased despite an ongoing series of incidents. The Inevitable Result Being: Yet another on-campus murder, repeated use of Unforgivables, a successful abduction attempt on Harry Potter, and capping it all off, the resurrection of Lord Voldemort.
Near the end of the book, Minister for Magic Cornelius Fudge is told that Lord Voldemort has regained his power. The evidence to support this includes the news coming from Albus Dumbledore, who isn't known for making stuff this serious up, and two testimonies. One of these is from a Death Eater who admits to having been in contact with Voldemort and working to ensure his return, and the other's from Harry Potter, who claims to have seen firsthand the ceremony that restored Voldemort to full power, and has the injuries to show it. As well as this, Professor Snape shows him a very clear Dark Mark on his arm. The last time it was easily visible was during Voldemort's reign of terror. You'd Expect: Fudge to figure out that with all this evidence supporting it, it's quite likely that Voldemort's back, and then take the actions suggested by Dumbledore to prevent him getting power and resources. Even if he doesn't believe it, he could still try and have the matter investigated, to confirm it for himself. Instead: Not only does Fudge take no appropriate measures, he somehow gets it into his head that Dumbledore's making all this up to try and take Fudge's place as Minister, nevermind that Dumbledore has never wanted the Minister's post as far as Fudge has known him, all because he doesn't want to deal with Voldemort's return. The result of this is that during the next book, Voldemort's side is able to operate quite freely, recruit the giants to their cause and break out a load of their supporters from Azkaban, while Fudge does absolutely nothing useful. Thankfully, Voldemort doesn't choose to focus all his efforts on taking over, but if he had, the situation could have become a lot worse. And when the truth does get out, Fudge is pretty much fired.
Order of the Phoenix
Voldemort is trying to lure Harry to the Ministry of Magic in order to retrieve a Prophecy about the two of them. His strategy is to use Legilimency to make Harry dream about the place, and want to explore it in person. Dumbledore realises this, and also figures out that Harry and Voldemort have a mental connection that Voldemort could use to spy on Dumbledore through Harry. In response to all of this, Dumbledore arranges to have Harry learn Occlumency, so that he can stop having these dreams. You'd Expect: Dumbledore to just tell Harry about the mental connection, the Prophecy and Voldemort's plans for retrieving it, and explain that this is why he has to learn Occlumency. That way, Harry might be more motivated to do so. Hell, Dumbledore had decided at the end of book four that the time was right to tell Harry about the prophecy. Instead: No-one tells Harry anything other than "you MUST learn Occlumency", "Voldemort might be able to read your mind, but not while you're at Hogwarts" and "There is nothing in the Department of Mysteries that concerns you". As a result, Harry doesn't take the lessons as seriously as the Order would like him to, remains curious about the Department of Mysteries related dreams he keeps having, and is surprised when the Order consider it a big deal that Snape's no longer teaching him.
Speaking of the above, Dumbledore's choice of Occlumency teacher also counts, as he pretty much admits at the end of the book. You'd Expect: Dumbledore to either teach Harry himself, or try and find someone else to do the job. Moody's a possible example; with his level of paranoia about pretty much everything, it's hard to imagine him not learning Occlumency to protect his secrets. For that matter, since Draco Malfoy proves its possible for a talented student to learn Occlumency over the course of one summer if he has a competent teacher and the decision that Harry needs to learn Occlumency isn't made until mid-term, Dumbledore has enough time to train literally anyone else in the Order of the Phoenix to be an Occlumens from scratch, and still have them finish teaching Harry before end-of-term. Instead: He gets Professor Snape to try and teach Harry Occlumency, a magical art that is based on controlling your emotions, when the two of them have a longstanding mutual hatred and visibly cannot so much as be in the same room without enraging each other by their very presence. Unsurprisingly, this crashes and burns.
Since the beginning of the year the Ministry of Magic has been steadily antagonising Harry and DD, painting the kid as a liar and a madman in media and staunchly refusing to accept Voldemort's return. Then a Ministry official, Dolores Umbridge, is appointed the DADA teacher at Hogwarts, and at her first lesson she makes it perfectly clear that she's upholding this policy. You'd Expect: After this first lesson at the least, Harry would try to keep his mouth shut, since, frankly speaking, he has no proof of Voldemort's return, and won't achieve anything by proclaming it again. Or: He could've countered Umbridge's assurances by mentioning Sirius. After all, the Ministry couldn't deny his existance, and they did fail to capture him, so they couldn't deny he was a threat either. Instead: He tries to claim that Voldemort has returned, with no proof other than his word. He doesn't convince anyone and ends up with a week of detentions.
During said detentions, Umbridge forces Harry to magically carve the words "I must not tell lies" into the back of his hand. You'd Expect: Harry to inform professor McGonagall and, for his next detention, take her (or anybody else) with him under the Invisibility Cloak. You'd think the Ministry, even in its newfound Jerkass mode, would hardly be able to get away with mutilating children. Instead: He suffers silently, not wanting to give Umbridge the satisfaction of seeing him complain, and lets her continue her reign unchallenged.
Cho Chang decides to join the illegal defense group Harry had set up under Professor Umbridge's nose. She also has a friend called Marietta Edgecombe, whose mother works at the Ministry of Magic, and would therefore be likely to lose her job if her daughter got on the wrong side of Umbridge. You'd Expect: Cho to either keep Marietta in the dark about the group, or tell her about it, but not put her under any pressure to join. Instead: She makes Marietta come to the meeting with her (her words), effectively lumping her with the group whether she likes it or not. Things are all well and dandy for about six months, but then Marietta reports the group to Umbridge, and Dumbledore is forced to take the blame for it to protect all the students involved. Marietta meanwhile is left disfigured, and viewed as a traitor, as a result of her "betrayal", whereas Cho - who was technically responsible for all of this - faces absolutely no consequences as a result of her actions.
And then there's the matter of the organisation itself. It's founded by Hermione, who has a list of all the organisation members, entitled "Dumbledore's Army". That is, as incriminating an evidence, as they get. You'd Expect: That she would keep it hidden, keep it on her person at all times, or at least put a spell on it that turns it blank to the univited eyes, the same one students have been placing on a restricted magazine that same year. Instead: She keeps in their training room, without any concealment. When they are busted, the list is used against them.
Harry gets given a package from his godfather, who implies that Harry can use it to keep in contact with him while he's at Hogwarts. You'd Expect: That Harry would at least have a look at the package, to see what it is, even if he doesn't plan on using it. Instead: He doesn't, apparently afraid that if he so much as opens it, his godfather will get in trouble. It turns out to just be a magical equivalent of a walkie-talkie. Result: Whenever he wants to talk to his godfather, he has to break into Umbridge's office. You'd Also Expect: That the first time Harry did this, Sirius would tell him to use the mirror, so that they can talk safely in the future. Instead: Sirius never gets round to it. You'd Also Expect: That the Order in general would take care of providing Harry with means of emergency communication, not to mention extraction. They know that the boy is a trouble magnet, and that the enemy is after his head. Instead: Nobody gives a damn, except Sirius, and he has such a... peculiar way of doing things, that of course it leads to a disaster.
Professor Umbridge gets Snape to give her some truth potion, which she plans to use to interrogate Harry on the location of two of his most important people, both of whom are fugitives. Snape, who is a renowned expert in the field of potions, tells Umbridge that she only needs to use three drops of the stuff for it to work. You'd Expect: Umbridge to remember this when the time comes to do the deed, especially since Snape is a potions expert and she is not. Instead: She uses up the whole bottle. Worse, it's Snape's last sample of that potion, and it takes a month to make. The result is that the next time she needs it, naturally there's not a drop in the castle. And On Top Of That: She not only pours the whole bottle into Harry's drink, she then fails to make sure that Harry actually drinks it. Harry defeats her by the simple ruse of raising his cup to his lips but not actually opening his mouth, and Umbridge — despite looking directly at him the entire time — unaccountably fails to notice that Harry is not swallowing anything, and that Harry's robes are stained from where he spilled some of the tea on himself to lower the liquid level in his cup.
Hermione and Harry manage to lure Umbridge into the Forbidden Forest by claiming that Dumbledore is keeping a weapon hidden there. The trio are then confronted by the resident herd of centaurs, who generally don't take kindly to wizards intruding in their territory. You'd Expect: Umbridge to decide that staying alive is far more important than fulfilling her Fantastic Racism quota for the week, and not do anything to provoke the centaurs. Instead: In a supreme display of being Too Dumb to Live, she repeatedly insults and tries to boss around the huge herd of centaurs surrounding her. The herd promptly drag her off into the forest, and while we don't see what happened to her after that, it was rough enough to give her PTSD.
Right after the above scene, the centaurs are deciding what to do with Harry and Hermione. One of them points out that they bought Umbridge here, and that Harry is nearly an adult, implying that they won't have to worry about breaking their rule of not hurting children. You'd Expect: Hermione, who is typically very knowledgeable about the wizarding world in general, to remember that a major Berserk Button for centaurs is the idea of serving wizards, and therefore say something along the lines of "We were trying to find the giant, so he could get rid of Umbridge. We never meant to run into you guys!". Instead: She straight-up tells them that she was hoping they would deal with Umbridge for her. The centaurs, furious at being used, decide that Harry and Hermione can share Umbridge's fate, and the pair are only saved thanks to Grawp randomly showing up.
Voldemort lures Harry to the Ministry of Magic and sends his goons there to retrieve the important Prophecy that only Harry can touch. You'd expect: Lucius Malfoy, who's in charge of the operation, would only take those Death Eaters who, like him, had weaseled their way out of Azkaban and into the Ministry ranks, and thus would have a legitimate excuse to be there (or send only the escapees). Instead: He takes the recent escapees from Azkaban with him, so when the Cavalry arrives, his true allegiances are exposed. Additionally, he and his cronies only reveal themselves after Harry takes the Prophecy orb, and they can no longer shoot him with spells for the fear of breaking the orb.
During the events at the Ministry, we see that the Time Turners are kept on an open shelf, without any locks, guards or alarms and in a room accessible to a bunch of kids. The power to rewrite the timeline is there for the taking. You'd Expect: That of the numerous people who infiltrated the Ministery that night, someone, be it heroes or villains, would realise the tremendous potential and help themselves to a Turner or two. Instead: They are completely ignored.
The prophecy ball Voldemort wants is kept in the Department of Mysteries in the Ministry of Magic. It can only be obtained by himself, or Harry Potter. You'd Expect: That Voldemort would simply sneak in and steal it, seeing as Harry and 5 other kids practically waltzed in there undetected, despite the fact that Harry is high on the list of people the Ministry is against at the time. Instead: Voldemort decides that it is too dangerous to attempt this as he will probably be discovered and the world will know he is alive again. Naturally, Voldemort tricks Harry into stealing the prophecy, then the Death Eaters try to steal it from him before he escapes, and then Voldemort, who claimed it was too dangerous for him to enter the Ministry, enters the Ministry, just after the prophecy gets destroyed, revealing himself and making his plan less than useless.
Half Blood Prince
In Order of the Phoenix, Harry failed to listen to the advice of someone who was not only a good friend, but the most intelligent of his friends. When Hermione repeatedly told him that there must have been a good reason for Dumbledore to want him to learn Occlumency, and later, that his vision of Sirius being tortured was probably a trap, he angrily brushed her off, and his refusal to listen to reason ultimately culminated in his godfather getting killed and most of his friends ending up hospitalized. You'd Expect: That in the future Harry would at least give some serious consideration to the advice of a friend who could have saved him a whole lot of grief if only he'd listened to her from the beginning. Instead: He continued to brush her off when she repeatedly warned him about the fishiness of the so-called Half-Blood Prince, deciding that an easy Potions grade was worth more to him than the concerns of one of his closest friends. As a result, he ended up nearly killing a fellow student and landing himself in detention for the remainder of the year, and was unable to play Quidditch as a result.
And then the Half-Blood Prince's book itself. It had some unknown hand-written spells without any kinds of notes of what they actually do. You'd Expect: That a person, who'd been studying magic for six years and had more then once witnessed firsthand how dangerous and unpredictable it could be, would know better then to wantonly use unknown spells. Instead: Harry tries one of them in their own dormitory. Luckily, it turns out to be a type of levitation spell that yanks a person by an ankle and hangs them in the air, but otherwise does no serious harm. You'd Expect: Harry to take a hint, that some of the spells in the book are unsafe and discontinue such reckless experiments. Instead: The next spell he uses is denoted "for enemies", and he casts it during a school brawl. Lo and behold, it turns out to be an actual combat spell, and he very nearly kills a fellow student. You'd Expect: Harry to really take the hint and either destroy the book or surrender it to the teachers. It's not like he could've gotten into any more troubles than he already was in, and giving up the book could even be counted in his favor and alleviate his sentence. Instead: He hides the book, apparently intending to retrieve it once things calm down. Thankfully, one of the villains inadvertently burns the damn thing before any more damage could be done.
Following from the above Snape deserves a mention as well. Whether he just left the book in the school after he graduated from his classes, or it was actually given to Harry with his leave as a part of DD's next elaborate scheme to inconspicously supply the kid with the Luck Potion, You'd Expect: Snape to go through the book first and make sure it doesn't contain something as dangerous as "Sectumsepra". Instead: He doesn't.
And then there's the matter of the brawl itself. Harry is about to have the Cruciatis Curse cast on him by Malfoy. You'd Expect: Harry - who knows enough about Defence Against the Dark Arts to illegally teach it - to use one of the spells he knows (Expelliarmus, Stupefy, Levicorpus, Pertrificus Totalis, etc) to take Malfoy down non-lethally. Instead: He uses a spell he doesn't know the effects of. It turns out that it inflicts nasty wounds on a person, and as a result, Snape gets an excuse to give Harry a crapload of detentions that cause him to miss the last Quidditch match of the year, and stop him from being able to spend time with his girlfriend.
In this book we find out about Voldemort's set of six magical MacGuffins keeping him immortal. You'd Expect: He'd make them impossible to discover either by using nondescript objects that wouldn't stand out to someone or by hiding them in places only he knows about, that are unconnected to him in his history. In Addition: Since you don't actually have to have a Horcrux available to hand in order to use it to resurrect yourself, you don't have to worry about keeping it somewhere you can fetch it back from. So absolutely nothing prevents Voldemort from doing something like sealing at least one backup Horcrux into a 55-gallon drum of cement and then dumping it overboard at a random spot in the ocean. Or launch it into space. Instead: He uses rare and impressive artifacts and hides them in places connected personally to him, most notably, at Hogwarts, where most of his enemies have been for the past 6 books. And he hides them all in places that are entirely possible to walk to, with at most a few traps or guards between the Horcrux and the exit.
During Harry's lessons with Dumbledore, Dumbledore shows Harry a memory of Slughorn talking with the young Voldemort about "Horcruxes" and tells Harry that he believes the memory to have been tampered with and that it's important to get the real memory. You'd Expect: Dumbledore would tell Harry what a Horcrux is and why he thinks it's so important to get the contents of this conversation, particularly since he had previously promised to tell Harry everything he knew or even suspected about Voldemort's actions and plans. Instead: He doesn't tell Harry anything other than to get the memory, Harry doesn't place a very high priority on it, and several months are wasted.
Harry and DD infiltrate the vault where Voldemort's Horcrux is kept. The thing is lying at the bottom of a basin full of potion that cannot be removed by any means, other than drinking it. When Harry quite reasonably notices that drinking the potion's a stupid idea, because it's a potion made by Voldemort, DD reassures him that V would want to interrogate the intruder, so while the potion would most likely cause pain, weakness and other debuffs, it would not be lethal. He also insists that he (DD) has to be the one to drink it, because "he's much less important than Harry". You'd Expect: Harry would then just as reasonably notice that it's a tremendously stupid idea, because if DD is right, then there must also be an alarm to inform V about the intrusion, and he's either on his way to the cave or already there, waiting outside for DD to drink and keel over. Or at least there might be other wards installed to finish off the weakened thief. Obviously, in such situation it's a suicide to let DD drink the potion. Instead: He just goes along with it and only survives because of the point below. You'd Expect: The cave defence to actually work this way. There either should have been an alarm, or the potion should have been lethal. Or perhaps both. Instead: The potion causes a terrible thirst in the victim, wards prevent water from being conjured, forcing the victim to drink from the surrounding lake, which causes a horde of Inferi to rise up and drown the thief. Except that it doesn't work if the thief uses someone else to drink the potion and then simply prevents them from going for the water. You cannot even argue that V overlooked this possibility, because that was exactly how he tested the potion - by having someone else drink it. And since there're no alarms, nothing prevents the thief from leaving and returning with the spare. And the Inferi prove to be rather crappy guards, as DD, even in his weakened state, manages to fend them off.
As the expiration date of the Blood Ward on the Dursley's house grows near, the Order needs to extract Harry from his house and get him to safety, but Harry cannot use magic yet, and Voldemort's agents have already infiltrated the Ministry and passed a bill, prohibiting the use of Apparition, Floo Powder and Portkeys inside the house, ostensibly for Harry's safety. Not made it impossible, mind you, just prohibited. You'd Expect: Them to ask an Elf, be it Dobby, Kreacher, or any of the Elves employed in Hogwarts (which is by that point still under their control) to side-apparate Harry, since, as was shown in book 2, the Ministry cannot detect Elves apparating at all. Or have Harry put on his Invisibility Cloak and fly away. Or get him and an escort to leave like the Dursleys. Or simply use mundane transportation. What's Worse: Since the only reason Harry has needed to return to Privet Drive in the past is to recharge the Blood Ward for the next year, and there isn't going to be any "next year" in this case as this is the summer the Blood Ward is set to expire, there is no need for Harry to be in this situation at all. They could simply have evacuated the Dursleys six weeks early while sending Harry directly from Hogwarts at end-of-term straight to the Order of the Phoenix safe-house he was originally intended to go to, and so avoided this entire trap from the beginning. Instead: They go with Mundungus Fletcher's (secretly Snape's) plan that involves disguising six people as Harry, and having them, along with the real Harry flown to one of seven safe-houses, with just one escort each, giving the Death Eaters ample opportunity to attack them en route. Granted, they had the sense to try and lay a false trail, but they still avoided the much safer solution. They only barely make it, and it costs Moody his life, George his ear and Harry his owl.
Following Voldemort's takeover of the Ministry of Magic and Grimmauld Place getting compromised further, the heroes are living out of a tent, running low on supplies, have very limited access to research materials, and having to move frequently to avoid being found by Death Eater search parties. You'd Expect: They would remember that Voldemort's people only have freedom of movement within the United Kingdom as that is the only government Voldemort controls at this moment, and that there is no reason they have to stay in the country, just merely to visit it whenever they think they've found a Horcrux location. And simply relocating to France would allow them a safer territory to stay in, access to sources of supply, possible allies (such as Fleur's parents or Madame Maxine), and much greater access to research materials (such as the library of Beauxbatons). As to how they could get there? Wizards are demonstrably capable of Apparating from northern Scotland to London in a single jump, which is enough distance that you could hit Germany in a single jump from London, let alone France. Alternately, people who can turn invisible, shapeshift, teleport around security barriers, and rewrite memories don't have much trouble getting through Customs. What's Worse: Hermione's family takes vacations in France, the most recently being three years ago right before the Tri-Wizard Tournament. And its specifically lampshaded in the text that one of the reasons the Trio was able to use the Forest of Dean was because since Hermione had vacationed there when she was a small child, she remembered the place well enough to use as an Apparition destination! And yet she can't remember a place she's been to far more recently, because it would be inconvenient for the script if she did. Bleah. Or At Least: Hermione would remember that the muggle world is full of places where you can buy food — or, if you're worried about leaving a trail, you can use your magical wizard powers to steal food from after hours. Again, its not like people who can turn invisible, teleport, and trivially open any non-magical lock are short of options, and the Trio had already shown a willingness to 'midnight requisition' food from isolated henhouses and suchlike. Instead: The Trio consistently act like the United Kingdom is the only nation on the entire planet and never even idly ponder the idea of operating from a base area beyond Voldemort's span of control, despite easily being able to reach one. Likewise it is literally months before Hermione thinks to buy more food at a grocery, and even that only for a special occasion instead of as a regular occurrence.
Voldemort finds out that his wand and Harry's have identical cores, causing them to malfunction when used against each other. You'd Expect: Voldemort to let someone else kill Harry. It's too dangerous to risk going wand-to-wand against Harry personally when all it does is reflect your spells and cause Harry's own wand to become more powerful. Instead: Voldemort insists HE must kill Harry, and wastes time on futile schemes to find a loophole, such as using another servant's wand, or searching for the Elder Wand. So Harry survives. Again. And again. And again.
The bad guys at one point capture the heroes. You'd Think: Knowing full well that in the wizard world even the most innocuous tackle can be a magical artifact of unknown power, they would strip their prisoners of all possessions, down to the clothes. Instead: They content themselves with taking away the heroes' wands. Naturally the heroes have some spare artifacts that help them escape.
The heroes themselves aren't much better. Harry accidentally summons a load of bad guys by saying Voldemort's name. The bad guys appear, and aim their wands at the heroes' tent. You'd Expect: They would first try side-along apparating to a short distance away from the tent and the bad guys. They've got the hang of it by now, and they've used it to get out of a number of similar situations. For bonus points, they could then sneak up on the bad guys, stun them and leave. Lacking that, Ron and Hermione could've gone out and distracted the baddies, while Harry sneaks out under the invisibility cloak and then snipe them all. Instead: Hermione uses a spell to disfigure Harry's face, to prevent the bad guys from identifying him as such, and they try to talk themselves out of the situation. They fail, thanks to the fact that one of the Snatchers sees Harry's scar on his forehead, and the gang are taken to Malfoy Manor. Hermione endures a brutal interrogation and Cold-Blooded Torture there courtesy of Bellatrix and Dobby dies trying to break them out.
The fact that Harry summoned them by saying Voldy's name despite having been previously warned that it had been jinxed and shouldn't be spoken out loud (and had even been reminded of it right before he said it!) is another example of the trope.
Voldemort realises that Harry has gone Horcrux hunting and checks several vaults, finding them all ransacked. You'd Expect: Voldemort would keep his snake Nagini, who's also a Horcrux, by his side at all times, and preferably under magical protection. Instead: While he does both these things, he removes the protection on Nagini when he thinks he's won, even though the battle at Hogwarts hadn't even ended. The result is Nagini dies, and Voldemort loses his immortality and is then killed.
It's even worse in the film, where he makes Nagini fight the good guys without even re-placing the protective magical cage on her.