- Thanks to L's initial investigation, the police force deduce that Kira needs a face and a real name in order to kill someone.
You'd Expect: For them to report this fact to the government and persuade them to either blur out the suspect's faces during any past reports or not reveal their full names to the public during a live report in order to minimize the rate of Kira-related murders. If the Kira murders continue to rise due to internet, then the police try and trace the suspect whoever hacked the criminal database and potentially find the culprit.
Instead: Nobody considers doing any control in the Kira killings and the death tolls continue to rise with no-one being able to identify the culprit for 5 years. By the time it's considered, it's a bit too late, and Kira no longer cares about if the named offenders are guilty or innocent.
- Light starts killing dozens of people with the titular artifact, which requires knowledge of the victim's name and face. Shortly afterward, Interpol makes a broadcast wherein "L", the greatest detective ever, announces that he will be taking the Kira cases. More importantly, he does this while giving his real name and showing his face for what is supposed to be the first time ever, and is practically daring Kira to kill him right then and there. There is something suspiciously fishy about this.
You'd expect: Light to realize this is likely to be a trap or probe of sorts and avoid killing the man. Or, if the temptation is too strong, do some research on the name and face to check if its falsified first and then kill him at a later date.
Instead: He writes his name in the Death Note right then and there and, big surprise, it is a trap. Now, not only has L figured out his MO and limitations, but has also pinpointed his general location.
- L himself falls into this during the exact same moment. He sets up a trap to pinpoint Kira's location to specific regions of the world. When the double for L dies, L's trap works.
You'd expect: That L would come forth to only Interpol and the local police with the information that he has learned from the broadcast, explaining the trap to bait Kira out and that with it, he has narrowed Kira's location down to the Kanto region of Japan. Thus, having successfully baited him into revealing his location, MO, and limitation, he would lower Kira's guard down so that he could then trick Kira into revealing information known only to them and the criminal (a common police tactic in real life.)
Instead: He taunts Kira by explaining everything he just did and what he just learned. Thus, this not only reduces the information that can be used to convict Kira (as millions of people just learned it) and forces Kira to up his guard, but also potentially destroys the trap's very purpose, given that from L's perspective, Kira now might perfectly opt to abandon Kanto and retreat to any other place of the world where he will not fall for the same trick again. Light could have been caught entirely by surprise without Near and Mello having to get involved had L not dumped a bunch of evidence that could easily be withheld from the media onto his lap and bragged how he just trapped him.
- After his first attempt to kill Near failed, Light Yagami sends the Death Note to Teru Mikami, a definite Kira supporter, with instructions on it.
You'd Expect: Light to send a message to Mikami to hide a page of the Death Note on his person, considering he must have had Kiyomi Takada do the same herself, and does so himself (using a trick watch to hide it). This would help him handle emergencies, the number of which had lately been high enough for Light to be tempted to kill Sayu with the watch trick. Additionally, for himself, he would make some extra precautions to ensure that he's not on the brink of defeat again.
Instead: He does not. This is clear from the fact that Mikami has to go to the bank a second time in a single day in the first place to kill Takada. Light, blinded by his ego and not even instructing Mikami earlier to only enter the warehouse (which has a single exit to begin with) upon hearing a password from him (like what he did in his Memory Gambit), declares his victory in the warehouse too early.
- Raye Penber is an FBI Agent currently tailing Light Yagami. While tailing him, the bus he and Light (and Light's date) are on gets hijacked by a known criminal. Light says he has an idea, but needs to know that whoever is behind him (Raye) is someone he can trust and not an accomplice of the guy. (Unbeknowst to Raye, the entire hijacking is a plan devised by Light to find out his name and face)
You'd Expect: Raye Penber, as an officially trained FBI Agent, to know what a stupid idea it is to give his real name and identity to a target that is currently under suspicion of likely being connected to a mass-murderer and perhaps show him a Fake ID or an FBI badge to him giving him proof of his validity while concealing his true identity at the same time.
Instead: He freely shows his ID to Light, giving him his real name and face to deal with, which ultimately allows Light to manipulate him into finding out the names and faces of the other FBI Agents currently in Japan for the Kira case and get them killed.
Additionally: This also (indirectly) results in getting his own fiancée killed.
- Shortly after Raye's death, Naomi Misora has just found out a piece of crucial information regarding the Kira case and decides to report it to L regarding this. The task force is unfortunately busy when she checks in with them. However, suddenly he is intercepted by Light Yagami and after she gives out a false name, decides to follow her for some reason. What she knows is that he is the Chief's son, well-regarded in the office, and a figure that most people trust. Light bluffs that the task force is always closed off, that he is on the task force, and that he can get her on it to reveal her information.
You'd Expect: For her to quickly suspect that Light is Kira or at least realize that he is stalking her and tell him off. Failing that, she could knock him out with a capoeira kick and run as far away from him as possible to her intended destination.
Instead: She apparently suspects nothing wrong about the very man who followed him and worse, she gives away her ID to Light in spite of his behavior. She ends up getting killed for it and thus the potential information that could catch Kira is lost forever.
To Make Matters Worse: Light writes it in the Death Note that she will kill herself, in a way that no one will ever find her body. L, upon realizing she's missing, understands that she must be dead, but her parents don't. In the film adaptation, Naomi is smarter than this in not giving out her name, period, and suspects Light from the start. It's only by the fact that she and Raye had already planned out their wedding that Light had the presence of mind to find the church where the ceremony was planned.
- Light, still being a student, has been keeping his Death Note activities in the afternoon to late evening. L comments upon this, suggesting Kira is a student.
You'd Expect: Light would try and dissuade the notion by suggesting that it is just a coincidence and many people may only be able to attack in the afternoon, not just students, being the Chess Master he is. L's conclussion is actually rather feeble to begin with given how many jobs only allow for freetime in the afternoon.
Instead: He begins writing down names to die in a more spread out fashion that day the night before, leading L to deduce that the Kira has insider information about the investigation and prompting him to lock everyone in the same room together, which forces Light to actually get on the team to keep up with his opponent.
- It's the endgame! Light and Near face off in the ultimate battle of wits. The fate of the world rides on these moments. Light's plan? To perfectly recreate the act of using the Death Note with a fake, then ensuring Near swaps the fake for another fake. Essentially, they will have believed that they disarmed him, unaware that they've only captured a harmless copy! Meanwhile, he keeps the real Death Note hidden away, then replacing the fake with the real one at the last moment! That way, the copy they "know" is fake is anything but! That way, when they allow him to incriminate himself, he'll instead slaughter them all at once, and the world will be his!
You'd Expect: That Light The Chessmaster would keep an eye on the real Death Note at all times, test it prior to the epic finish, keep several backups stored, maybe lend that page he keeps in his watch to the assassin, and hey, maybe even a grenade or two just in case. As long as they die, however they die, he wins. And even if they don't, they won't have any evidence directly linking him to Kira.
Instead: He puts the original in a safe miles away, under no observation, doesn't bother testing it, and then loudly incriminates himself in front of all of them. Then he tries to use a Death Note (ironically, a functioning Death Note page that could have killed them all had he given it to his lackey instead), in front of several people with much faster guns. Twice.
- As bad as the above Death Note examples are, probably one of the worst moments of stupidity in the series occurs at the end of the Yotsuba Arc. The police have caught Higuchi, and neither Misa nor Light have any memory of being Kira, and thus they are not a threat any more. Suddenly, Soichiro and Mogi see Rem after touching the Death Note, and freak out. L asks Mogi to bring the Death Note over to the helicopter, where Light is sitting right next to him.
You'd Expect: That L, who pretty much figured out Light's Memory Gambit and told everyone on the task force about his suspicions regarding it, and who strongly suspected Light as Kira from the very beginning, would be extra careful with the Death Note seeing as how Light is RIGHT NEXT TO HIM and keep the Death Note away from him at ALL COSTS. Unfortunately, he gets distracted by Rem and the various realizations he has regarding her and the notebook, and Light impatiently grabs the notebook out of his hands. But even then, you would at least expect L to try to grab the notebook back from Light as soon as he regained focus and saw Light not holding the notebook, but also acting VERY strange with it. If Light resists, then L can just use that reaction as more evidence against him, and/or just ask one of the other task force members to hold on to it instead. Since the team will be regrouping back at HQ after securing Higuchi, L can read over the rules of the Death Note with the task force while keeping Light away and try to find out how to both solve the case and get rid of the danger posed by the notebook. Even if L doesn't know about all the rules of the Death Note or about the piece of the notebook in Light's watch, you would at the VERY LEAST expect that he would do everything in his power to ensure that Light and the Death Note stay separate and keep a watchful eye on both.
Instead: L just sits there as Light regains his memories. He simply asks Light if he is ok, and then reluctantly lets him look over some names from the Death Note. All he does afterwards is give Light a suspicious look, and then immediately goes back to looking at the police handling Higuchi.
- Even worse, shortly after Light has the Death Note, Higuchi suddenly has a heart attack and dies. This is obviously the work of Kira, and the entire task force knows it. What does L do in response?
You'd Expect: L would instantly put two and two together, realize "Hmm... that happened right after I let Light hold on to the Death Note for a while, and I pretty much figured out his whole memory gambit earlier. I guess that pretty much confirms he's Kira", and then put Light into custody until he can figure out exactly what happened and then come up with a plan to end this nightmare.
Instead: L pretty much lets Light go free as if Light is completely un-suspicious, and then lets Light continue his plan, which soon gets both L and Watari killed. Thus, Kira is free to wreak havoc on the world for another four years.
What An Idiot / Death Note