In Dance in the Vampire Bund, a Mina imposter has taken control of the Bund, and even after the inhabitants of the island have figured it out, the blood pact still forces them to obey her. When Akira figures it out and goes off to rescue the real Mina, the fake orders them to find and capture Akira. However her failure to specify "Half-German Werewolf by that name" means that they knowingly expend thousands of man-hours and vast amounts of equipment digging a half-Brazilian vampire named Akira out of his hiding place beneath the Bund.
In Eat-Man, the main character, Bolt Crank, will often take jobs from clearly evil people, only to later exploit extremely literal wordings in his contracts to mess up his contractors. Case in point: Bolt takes a contract from a group of greedy people to protect a girl whose blood is a potion of youth for a certain period of time. Bolt protects her... from those exact people.
For Negi's apprenticeship test, Eva gave the conditions "If you can hit Chachamaru even once with your Kung Fu, then you'll pass. The match continues until you're dead and you can't attack anymore." This backfires on her when she declares the match over after Negi was completely thrashed, only for him to stand back up, stating that there's essentially no time limit since the condition was "until I die".
It happens again later, when Setsuna says that she can't use the "Shinmeiryuu Hidden Technique, Zanmaken: Ni no Tachi" because only people close to the founding clan of the Shinmeiryuu are allowed to learn it. Jack Rakan gets around this restriction by renaming the attack: In Celebration of my First Kiss with Ojou-sama Special! Setsuna is (understandably) hesitant about using Jack Rakan's particular version.
Kongoh Bancholoves this trope. People tell Kongoh not to do something, ranging from "don't open that door" to "don't move your arms, legs, or head." He follows the orders to the letter, and still ends up causing lots of damage.
Earlier, Mao survives Lelouch's attempt on his life because Lelouch ordered the Britannian police to "shoot" Mao, not "kill" him, and, as a result, Mao gets better by the next episode. It doesn't explain how he survives several dozen gunshot wounds including from a Knightpolice unit (he points out that medicine these days is extremely advanced).
When Arthur the cat steals the Zero mask, Milly promises a kiss from a Student Council member to the person who manages to retrieve it. The school goes nuts chasing the cat in the hopes of getting a kiss from their favored Council member, but when Suzaku gets it (and Lelouch helps save his life), Lelouch's little sister Nunnally gives each of them a peck on the cheek and says "I hope a junior member is good enough for you."
A rather non-serious example in Rurouni Kenshin: during the fight between Sanosuke and Anji in the Shishio arc, Kenshin gives Sanosuke verbal encouragement. We then gets this exchange:
Yumi: Himura-san. That should be an one-on-one battle. You shouldn't be giving him a hand.
Kenshin: Yes. That is exactly why this humble one gave him an advice, not a hand.
When Yamamoto orders Kenpachi and Byakuya to drag Hitsugaya's Advance Squad back to Soul Society so they can't help Ichigo rescue Orihime from Hueco Mundo, Byakuya uses this trope to commit Loophole Abuse on Yamamoto's order. Since Yamamoto only ordered them to bring the shinigami back to Soul Society, Byakuya does precisely that... then promptly helps Renji and Rukia return to the World of the Living so they can go after Ichigo's group.
In anime filler, Byakuya admits to Muramasa and the rebelling zanpakutou that he's helping them to protect his pride. Helping them is the only way he can locate Muramasa's master, Kouga, who was expelled from the Kuchiki family for dishonouring the family name. By killing Kouga, Byakuya can restore the family's pride and honour.
In flashback, a young Uryuu argues with his father over Ryuuken's command to stop visiting Souken and Uryuu realises for the first time that Ryuuken hates being a Quincy. Ryuuken tells Uryuu "I have no interest and you have no talent." so Uryuu spends years thinking his father has no spiritual powers. At the beginning of the Arrancar Arc, Ryuuken uses his power to save Uryuu's life. Uryuu's surprise causes Ryuuken to invoke this trope: he never said he didn't possess Quincy powers, merely that he wasn't interested in using them.
There's the Water 7/Enies Lobby arc, where Robin betrays the Straw Hats because she knew they'd be exterminated by the CP9 and the "Buster Call" that had been placed under their command if they tried to fight. She gave herself up and willingly went to be executed with the promise that "All Straw Hats minus her would leave Water 7 alive". When they followed her to Enies Lobby, Spandam gave the order to kill them all.
Lucci: Our deal was that "All Straw Hats excepting you would leave Water 7 unscratched". And that's what happened.
Later, When Spandam, Lucci and Robin are fleeing the Tower of Justice in a secret passageway, Lucci notices that Chimney and Gonbe followed them and are hiding in the room. But because he has no love for Spandam (and possibly because he wants to fight Luffy,) Lucci keeps quiet about it until later, when they've gone to tell Luffy and he's broken into the passageway, explaining that Spandam ordered him only to protect him and nothing more.
Also, during the Marineford battle, Hancock attacks pirates and Marines indiscriminately, causing a Marine to ask her whose side is she on. She explains she agreed to fight Whitebeard and never specified that she would ally herself with the Marines and any man before her (minus Luffy but they don't know that) is an enemy.
Much earlier, Arlong promised Nami that if she brought him 100,000,000 Berries (the currency of the One Piece world), he would liberate her village. And it actually seems that he intended to keep his promise if she would one day present him with all these money. However, he never promised her that he would not steal all her saved money from her before she had collected all 100,000,000 Berries. And since he doesn't want to give away his rule over the village, that's exactly what he hires a corrupt Marine officer to do right before she has actually saved up enough money. Nami realizes what happened because said Marine makes the mistake of mentioning the exact amount of money.
In Puella Magi Madoka Magica, this is part of Kyubey's way of operating, combined with You Didn't Ask. He never outright lies. When Kyoko asks him if Sayaka can be restored to normal, he says it's never been done before. It's never been done before because it can't be done, but for the purposes of his plan he needed to lure her into trying anyways. He also says that he wouldn't be surprised if a magical girl succeeded in reviving another... except his species can't feel emotions, surprise being one.
In Kaiji, after exposing Ohtsuki's 4-5-6 dice, Ohtsuki tries to desperately grasp a way to not lose and says that since his last roll was interrupted by The Reveal, the dice didn't count, so he technically wasn't cheating. Kaiji offers him that last roll as a 4, saying that each of his cohorts will also roll trick dice. Ohtsuki accepts, thinking at most he'll only lose 1 million. Using a t-bone, Kaiji made a set of dice covered in ones. Meaning every roll will be snake eyes, resulting in a 5x payout to the roller. Ohtsuki is in no position to retort against this.
In Dragon Ball Z, for a Saiyan to become a Super Saiyan their heart needs to be pure. Son Goku, the protagonist, is the first to achieve this as he has not a speck of evil in his heart. Some time later his greatest rival Vegeta, a villain, also becomes a Super Saiyan since his heart is pure evil (stated in the manga version only). Vegeta wasn't really pure evil anymoreby that point, but he believed he was and apparently that was close enough.
In the same saga, the heroes demanded Androids 19 and 20 fight them somewhere deserted to avoid bystanders getting in the way. 20 decided to make a deserted area by vaporizing half the city with his Eye Beams.
Goku: Leave these people out of this!
19: There are no more people left to leave out.
In Yu-Gi-Oh!, when a Sadist Teacher discovers a love letter to a girl in her class, she tells the sender to admit the deed and she will let them off if they do. Yugi stands up to admit that he wrote the letter and Jonouchi/Joey confesses that he put it in her desk, with Honda/Tristan saying that his feelings were in that letter. The teacher points out that only one of them could have done it but Jonouchi replies that none of them are lying. All three were technically telling the truth. Honda had a crush on the girl and asked Yugi to write the letter and had Jonouchi slipped it into her desk.
Yugi himself does this a few times too. For example, in the anime, he taunts Panik with his Swords of Revealing Light card, and then sets a card. When Panik tries to destroy it with his Reaper of the Cards (assuming that it's the Swords card), Yugi reveals it to be Spellbinding Circle. (He tells Panik that he never said it was Swords, he merely assumed that. The Spellbinding Circle was set to draw Panik's fire, because he figured Panik would try to destroy it.)
Suicide Island: In the first issue, patients who have attempted suicide are offered a choice to live on or die. A number of patients choose to die. They sign some papers and are put to sleep with drugs. They regain consciousness and find themselves on the title island. A sign nearby posted by the Japanese government states that everyone on the island is now an Un-Person and essentially "dead" to the government, and they can do whatever they want on this island, as long as they don't try to leave.
In the Bakuman。Show Within a Show, "Otter no. 11", this happens when Otter #11 does a misleading TV commercial for Flat Sail Marine Industries, which imports seafood from China and tries to pass it off as domestic. Ultimately, however, the commercials work because people think they're funny, rather than their being fooled by the exact words.
Otter #11: Sir, is this okay? Saying "this country's clams are delicious."
President: "This country" means China. We didn't say it was Japan.
In the Haruhi Suzumiya novels, this is how Kyon figures out the mystery in Remote Island Syndrome. Koizumi asked Yuki what the victim's body temperature was when they found him. He could have just asked "when did he die?" but didn't, since he knew she'd answer "he's not dead". The anime went in a slightly different direction.
Fist of the North Star has Kenshiro abuse this trope to inflict punishment on some deserving thugs in the anime. A bandit leader is rounding up men to engage in a primitive Blood Sport for his amusement, and one of the thugs in charge happens to tell a disguised Kenshiro to "Kill whomever you want! Punch them, kick them, throw them!" Naturally, Kenshiro proceeds to punch and kick the bandit who just spoke to him. When the bandit demands to be put down quickly, Kenshiro also complies. By dropping him onto his knee...so violently that his head explodes. Doubles as a Pun in the English translation, since 'put down' can mean 'release,' but can also be taken to mean 'kill' when applied to animals such as rabid dogs, which Kenshiro compares thugs to on a regular basis.
At one point in Speed Grapher, Tatsumi poses as Kagura's tutor, and when the chauffeur picks him up, he asks what happened to Ms. Wakaba, the girl's usual teacher. Tatsumi replies by saying "She got a little tied up", and the scene then cuts to the interior of the school, where poor Ms. Wakaba is seen Bound and Gagged inside a locker.
In Scrapped Princess it is prophesied that the newly born princess is "the poison that will destroy the world", and she is to be immediately executed. Well, she wasn't. It turns out that the prophecy is 100% correct if you only look at the situation from outside of the world. Her DNA is the key to unlocking the prison that the remnants of humanity are trapped in, thus "destroying" the world they knew and giving them access to a much larger one (the rest of the Earth).
An example in Magic Boy BT: BT tells Akagawa that "I saw Kuroyama putting a bug in your clothes". What he meant was "I saw Kuroyama putting a dragonfly in your shorts. What, you thought I was talking about the very aggressive wasp that stung you? The one I put in your pockets?".