What an Idiot!/Anime and Manga/Death Note

For a show that is supposed to be about geniuses, there are a number of noticeable idiot moments in Death Note.

Anime

 * In the second episode of Death Note, 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 practical daring Kira to kill him right then and there. There is something suspiciously fishy about this because why would an American detective be interested in a Japanese murder wave?
 * You'd expect: Light realize this was 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 it's falsified first and then kill him at a later date.
 * Instead: When the detective accuses "Kira" of being evil, writes Lind L. Taylor's name in the Death Note right then and there and, big surprise, it was a trap. Now, not only did L figure out his MO and limitations, but he pinpointed his location.
 * 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. Soichiro then discusses this at home, since Light likes hearing about his job.
 * 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 Chessmaster he is.
 * 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.
 * L calls his contacts from the FBI to start following members of the Japanese police. Agent Raye Penber is assigned to follow the Yagami family. Ryuk notices him trailing Light and warns him.
 * You'd Expect: Light would...do nothing and act natural. He has been very careful to appear as an innocent high school student bound for a prestigious university. Raye even notes to himself that Light seems to be an ordinary kid and that L must be overly cautious. The agent prepares to stop his investigation and write a report to L that Light is harmless.
 * Instead: Light writes in the Death Note that a criminal will hijack a bus while he's on a date with his girlfriend Kiyomi Takada, as a means to force Raye to reveal his name. To send a middle finger at L, he then uses Raye to find out the other FBI agents on the case and murders them as well. Light thinks that somehow this will cause a divide and conquer strategy, allowing him to find L using the Japanese police.
 * The Result: While the FBI pulls out of the case because Light's machinations lead to him killing twelve agents, L gets a lead: the families that Raye followed must have Kira in their midst, including the Yagamis. Soichiro is shocked but insists that they trust L and bug the Yagami household, to make sure that no one in his family is a killer. While the bugging doesn't work, Naomi Misora, Raye's fiancee and one of L's close friends, goes missing. L knows that since Naomi is FBI as well, she would have done anything to avenge Raye, and logically concludes that Kira must have killed her. By process of elimination, he figures out that Light is the most likely suspect since he trusts Soichiro, the mother is a homemaker, and Sayu is a sweet kid whom in Soichiro's words would feel extremely guilty if she ever killed a criminal. Cue L enrolling at the same university under a fake name and befriending Light to gain more evidence, while baiting him.
 * During said bus jacking, Raye prepares to compromise his trailing mission to save everyone being held hostage, including Light. When seeing that Light passes a note to Kiyomi saying he'll try to tackle the bus jacker, Raye informs him quietly that's not a good idea. Light accuses him of being an accomplice, that his dad said most hijackings have two people.
 * You'd Expect: Considering that Raye is technically undercover, he would have a fake ID on hand. As far as the world knows, Kira needs a name and a face to kill given that he or she wasn't able to kill L.
 * Instead: Raye gives his real ID, under the logic that if Light were Kira, he would have killed the bus jacker already.
 * The Result: He gets killed, mere months before his wedding.
 * The way that Light treats Matsuda also counts as this. Matsuda is the youngest member on the taskforce, who often brings up the opinions that no one wants to hear, such as that Kira's influence has reduced global crime.
 * You'd Expect: While on the task force and through the series, that Light would work on Matsuda to poison his mind, and turn everyone against each other.
 * Instead: Light assume that because Matsuda is an "idiot" in his and L's words, that he would easily sway to Kira's side. He only focuses on fighting L and L's successors Near and Mello.
 * The Result': Turns out that Matsuda is only stupid by the task force standards, considering he qualified in the first place, and he's sincere when he silently promises to find Kira after Soichiro dies rescuing his daughter from Mello. Also, he's a good shot and super-observant, which was how the task force got an in to a corporation using Kira for business purposes; he's also the one who saw where Mikami kept the real Death Note and switched it with a fake. In the climax, Matsuda ends up being the one who shoots Light multiple times after the latter tries killing the task force; the only reason he doesn't kill Light is the other cops hold him back as he shouts that Soichiro believed in his son's innocence, and he's betrayed that Light was an Ungrateful Bastard.
 * After his first failed attempt to kill Near in Death Note, 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.
 * 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.

Live-Action Film Series

 * Death Note: The Last Name
 * In the climax, L reveals to Light, after the latter prepared to murder his father, that he faked his death. He also proceeds to reveal that he proved Light was Kira, in front of Soichiro. The task force shoots Light before he can use his stray bits of paper; when he rants about how unfair the world and justice system is, Soichiro angrily agrees but points out that killing people to achieve that goal of perfection is not the right way to correct an imperfect society.
 * You'd Expect: Light would realize that he lost, and surrender. Due process means that he won't get killed, and he can figure out plan B. Or give the Death Note to Ryuk and relinquish ownership.
 * Instead: He calls for Ryuk, shouting at him to kill everybody. Ryuk said that he would be the one to kill Light when the latter stopped being entertaining.
 * The Result: Ryuk doesn't like the audacity of Light trying to order him to kill others. He writes only one name: Light Yagami. As he puts it, Light is no longer fun, and he doesn't want to wait around for the guy to either serve his jail sentence or bleed out from his wounds. Cue Mass "Oh Crap" from Light, a handcuffed Misa, and Soichiro as Light begs for his life from Ryuk and the heart attack starts.