An exchange in the twelfth Dragon Ball Z movie is an example of this:
Vegeta: Fuse with you? I'd rather die! Goku: Vegeta, you're already dead.
Another moment takes place between Chi chi and the Ox-King in the Cell Saga right after Gohan transforms into a Super Saiyan 2. The moment also borderlines on Dramatically Missing the Point had it not been for Chi chi's exaggerated tantrum that she throws during it.
In the horror manga Emerging, the protagonist starts celebrating when the lab results confirm that the deadly disease rampaging through Tokyo is not Ebola... until his partner informs him that the news means they're dealing with a completely unknown new viral pathogen.
Natsu from Fairy Tail is liable to do this. For example, at one point all of the denizens of a cursed village uncovered their arms and legs, which were developing into talons. Natsu was more impressed by the headman's large sideburns.
To give just one example: Sōsuke single-handedly creates a revolutionary suit of Powered Armor and puts it on the open market, but he fails to sell more than a small handful and ends up having to eat the cost of the rest. He can't understand why more people aren't interested in such a useful tool...never realizing that it's because he made the suit out of a cutesy theme park mascot costume named Bonta-kun.
In the Beach Episode for Gakuen Babysitters, Kamitani-sensei attempts to get the boys to compliment Inomata when she returns in her new swimsuit, implying that they should say something to her. Kamitani fails to grasp her intentions and responds with his usual bluntness ("Oh, it's a swimsuit."). While Ryuuichi initially appears to avert this by saying that the swimsuit is cute, it becomes apparent that he's literally complimenting the swimsuit, rather than her, when he makes an addendum commenting on the matching pattern with Kirin's floatie.
The foundation of Nozaki and Sakura's relationship, at least regarding... their relationship.
Nozaki is really poor on perspectives, and screws up on the characters' heights. When Hori points this out, Nozaki says different characters were standing on Scully Boxes in all the scenes. Hori then complains that nobody will carry boxes with them all the time, and Nozaki responds that he'll just have them say boxes are popular in-universe at the moment.
In Gintama, Gintoki and Kagura are so prone to this in Shinpachi's presence that it frequently seems like they're doing it on purpose just to drive him up the wall.
In Gundam Build Fighters Try's final episode, Minato Sakai is making a big fuss in the Meijin Cup due to the fact that he lost to Yuuma Kousaka. The entire time, despite having at least three people yelling it at him, he doesn't realize (or probably care) that the reason he lost was because his entry is based off of Fumina Hoshino (his one-sided crush) and he didn't even bother to get her permission to use her likeness, as evidenced by the fact that she's utterly humiliated and mortified by the model. He's just angry that Yuuma won and he didn't and really doesn't see the problem over what he built. This is reinforced by Expanded Universe materials like the OVA Island Wars and the Build Fighters toy line, which show that he just keeps making "Super Fumina" models despite the most famous and important Gunpla builder person in the world chewing him out for how wildly inappropriate it is.
Issei:(as he lies dying on the ground) If you're going to kill a guy...you should at least let him fondle your breasts.
THE iDOLM@STER- When the girls just received news that they need to retake their promo photos, Haruka gets nervous and the following happens.
Chihaya: Haruka, what's wrong?
Haruka: My heart will leap out of my chest at this rate.
Takane: That's terrible. (gets up from her seat) We need to call an ambulance right away.
In Inukami! both Keita and Youko have mortified expressions as Kei tells them about how her family made a deal with a shinigami for the great wealth but in turn the shinigami kills their offspring once they reach adulthood. They're horrified because they simply can't believe someone that looks as young as Kei is almost 20.
InuYasha: A demonic witch kidnaps Kagome so she could use her to transfer her spiritual power into a copy of Kikyo (Inu Yasha's late love interest) made from dirt and her buried ashes. When a part of her soul is transferred back into Kagome's body, she wakes up visibly shaken - not because she just had her soul temporarily torn out of her body, but because she had a bad dream that involved failing her math test. Cue looks of disbelief from Inu Yasha.
At the beginning of episode 7, Sharo wishes she could be as cool and confident as Rize. She then has an Imagine Spot of having the same confidence as Rize, and as she walks through a store holding a pistol, all of the other customers are understandably scared.
Near the end of episode 7, Cocoa, Rize, and Chino ask Chiya where Sharo lives because they wanted to give her some bread. Sharo then comes out of the dilapidated house next door. While Chino tries to apologize for assuming she was Secretly Wealthy, Cocoa instead asks Sharo where she lives. Sharo ends up having to point to that house she just came out of.
In Princess Jellyfish, Wholesome Crossdresser Kuranosuke falls over with a pain in his chest. The girls of Amamizukan, who think "Kurako" is a girl, pull down "her" shirt and are shocked to see fake boobs. Mayaya later tells Tsukimi about Kurako's treachery: she's really a flat-chested girl who pads her bra to look more attractive.
Lucky Star: Tsukasa and Yutaka seem to do this quite a bit in the manga.
Parodied in the first MegamiSoundStage of Magical Girl Lyrical Nanoha A's, which featured a part where characters submitted messages to be read aloud, typically their thoughts on the present situation or other characters. The somewhat ditzy Amy's message tells Nanoha and Fate to come straight home for snacks, and asks them to pick up juice and coffee freshener for her; she apparently thought the message to the audience was actually for Nanoha and Fate.
In No Game No Life, during a conversation about Feel and Kurami's backstory, Steph notices the ramifications of Feel's desire to end slavery in her home country.
Steph: An Upper Diet member planning to free the slaves... isn't that treason? (Sora, Shiro and Jibril gasp) That's really surprising, isn't it?
Sora: Yes. Steph, you were actually able to follow all that?
Merry shows Kaya Luffy's new wanted poster, and instead of noting that Luffy is now a wanted man she is excited to notice the back of Usopp's head in the corner.
Luffy does this all the time. Like his reaction whenever he learns that a bounty has been placed on him. On the other hand, most pirates do see their bounties as a sign of achievement, including most of the other members of his crew (any one of whom is more sane than Luffy).
The longarm tribe capture Brook and put him on exhibit. It turns out he's a really interesting sight...because he has one joint in his arm. Possibly a subversion because the entire tribe had two joints in their arms, but they still find that more interesting than him being a living skeleton.
Luffy tells his crewmates that he picked a fight with Big Mom (one of the Four Emperors). Understandably, most of them are shocked (except for Robin, who just smiles). Princess Shirahoshi is in awe of Luffy's "bravery" and says:
Shirahoshi: Oh my! You're so strong, Luffy-sama!
Usopp: That isn't the problem here!!
In the final chapter of Ouran High School Host Club, not only does Haruhi reveal the fact that she is a girl to the club customers, but they also find out that she and Tamaki are now officially a couple. However, it isn't until an outburst by Haruhi's enraged father that they fully grasp what was going on. Until that moment, they had simply assumed that Haruhi was a male (and very feminine) crossdresser...and that "he" and Tamaki were gay.
When Kyoya's father slaps him for being part of the Host Club the other members are shocked. Hunny was upset for a different reason:
In the Panty & Stocking with Garterbelt episode "Sex and the Daten City", during a swanky premiere for a film she and Stocking are in, Panty screens her "debut film" that she considers to be her award-worthy magnum opus. It turns out to be a pornographic flick, which threatens to flush her celebrity lifestyle down the tubes.
Mick: Your debut film is porn! You made a sex tape!? Panty:WHAT?! Serious?! So it was just direct-to-video?! Well, that explains why it haven't won an Oscar yet!
Possibly a minor example from Pokémon in this exchange between Roark and his father, Byron, after they enter the room where Team Rocket has stolen Byron's fossils, but all Byron notices is that there's one well-dug hole in the center of the room. Roark points out the room, but Byron only sees that there's a second, less-well-dug hole.
Roark: Hey, Dad, you'd better look over there. Byron: Closer examination reveals this hole was dug by a machine. (everyone Face Faults) Roark:CAN'T YOU SEE ALL OF YOUR FOSSILS HAVE BEEN STOLEN?!?!
Another repeating example is the Team Rocket trio not thinking about how rare a Pokémon is, but what Giovanni can use it for. He may not want to use it for that purpose, but they (mostly Meowth) are too single-minded to realize that.
In the first season, Ash finds a man who has the same picture that Sabrina had in her room. Ash concludes that he must be a photographer. When he later says that he knew Sabrina since she was a little girl, Ash figures he took her baby pictures as well. (What makes this rather absurd is that the guy is trying to help Ash in order to help his daughter, who has become evil and insane because of her Psychic Powers; you start to wonder why exactly he's so reluctant to flat-out explain who he is.)
More recently in the Best Wishes season. The cast meets the character of the day which has a double identity, which is VERY obvious. Iris, Cilan, Pikachu and Axew spot it right away, yet Ash misses it, not until he was told about it that he realized.
When Mii is separated from her sisters in episode 3 of Popotan, Mai wonders in horror what kind of men she might meet all alone in the street.
In the first episode of Sakura Trick, when asked to get (instant) yakisoba, Yuu instead buys yakisoba-flavored snack sticks.
In Saki in one chapter of Saki Biyori, the girls from Miyamori are planning to go shopping for summer clothes. Toyone, hearing that the day will be hot, points out that she doesn't have any summer clothes, prompting Kurumi to mention that it's why they're going shopping. Toyone is about to go out and buy some clothes so that she has something to wear while shopping for clothes with her friends when Kurumi stops her.
Also, slightly better case, in Gurren Lagann The Satire: After Kamina's death, Simon had trouble dealing with it, leading Kittan to attempt to encourage Simon by saying "He avenged himself! How many people can say they did that?" to which Simon replies "Not Bro, 'cause he's dead", after which Kittan outright says "YOU'RE MISSING THE POINT!"
In Tiger & Bunny, Fire Emblem declares that he, Blue Rose, and Dragon Kid are about to demonstrate some serious Girl Power. Blue Rose points out that one of these is not like the others.
Keith: Why, you ask? It's because this place has the most delicious lemonade in the city!
Once again, Keith is the source. Agnes calls the Heroes and tells them she's worried since Barnaby missed a meeting with her about hosting a dinner show. Keith shares her concern: can Barnaby really host a dinner show?
Welkin in Valkyria Chronicles is famous for these moments. In one instance, he tells Faldio to put a shirt on, not because Alicia told him so, but because he doesn't want him to catch a cold, and another instance when he asks when "the best time is to run away" before the Imperials sack their town. These bring out a lot of Alicia's Tsundere traits really easily...
During the Waking The Dragons story arc in Yu-Gi-Oh!, Yami loses a duel against Raphael, one of Dartz's henchmen. When the cast calls Kaiba and informs him of this, also telling him that Yugi's soul was taken, Kaiba freaks. Not because of Yugi's soul being stolen, but because Yami lost to someone other than him.
This one does make sense sort of, since Kaiba remained a Flat-Earth Atheist in not believing in any of the supernatural aspects of this particular children's card game (in the dub, that is), even though by this point in the series it's been pretty obvious that it does exist.
Yugi's the King of Games. When he loses, you know shit hits the fan, lost soul or not, because the whole show makes card games Serious Business.
Two Breast Expansion fetish mangas explore this concept with hilarious or saddening results:
In one a loli girl insecure about not developing, and thinking her boyfriend wants big-breasted girls (he actually only wants her because she's a flat-chested loli), gets basketball-sized breast implants...her boyfriend hates it and throws her out. The girl suspects it's because she's still too small and at the end she gets even bigger ones to try and please him. The second pair is bigger than her entire torso. At the end she struts arrogantly out of the clinic, boasting about her new size, only to fall over under the weight and find that she can't lift them, and ends up looking ridiculous.
In another a flat chested girl gets rejected by breast obsessed boys, who only care about busty anime girls, one time too many and gets huge breast implants to try and meet their standards...but when they see it "in the flesh" they're so comically huge that they get squicked and reject her again. So she goes off and gets bigger ones, and they still reject her. At the end she once again thinks she's "too small" and has gotten even bigger implants, this time almost too big to move, hoping this will do the trick...
Katarina in Destruction Flag Otome thinks she's the story's villain and judges everything based off of whether or not she's managing to avoid the bad ending in store for her. Unbeknownst to her, she actually avoided all the bad endings the moment she realized the role she was in, but now she thinks the best way to prepare for the future is to learn how to farm, build toy snakes, spoil her little brother and play matchmaker for a girl that is quite openly in love with Katarina herself.
A chapter of Daily Life with Monster Girl featured Ren Kunanzuki, a member of Rachnera's previous host family (the one who sold her off to the shady director). After completing many trials set up by the other homestays, Ren pleads her case to Kimihito, saying that she wants to overcome her challenge and be a family with Rachnera once more. As expected, Kimihito not only turns down her request, but also admonishes her for seeing Rachnera as an obstacle rather than a family member. However, Ren completely misunderstood the point Kimihito was trying to make and rushes out of the house, vowing the over come the "challenge" he gave her.
In Comic Girls, Koyume gets color pages for her manga, and the other girls are happy for her as they admire Koyume's illustrations. Ruki and Kaos quickly notice that the male lead looks just like Tsubasa, the object of Koyume's affections. Tsubasa, however, doesn't notice this, and wonders why the boy looks so feminine.
My Roommate is a Cat: Haru spends some time not being aware that "Haru" is her name, instead thinking it means "food" due to having heard it a lot from a human who would feed her as a stray. Ironically, her owner made it her name because she responded to it more visibly than to other names he tried calling her.