Dojima, the player character's uncle, finds a letter addressed to said character from a serial killer who's had the local police department tied up for the whole game. This letter telling him, basically, that if he rescues any more people then somebody close to him will die. You'd expect Dojima to watch his own family, the only people who could possibly classify as "close to [the player character]", while learning the truth about what's going on from his nephew. Instead Dojima admittedly tries the latter... By taking his nephew in to the police station, thereby taking in for interrogation the only person he knows could logically not only not be the murderer, but may well be the only one who can stop the murders. During this, he leaves his daughter Nanako home alone... As in a person who perfectly fits the bill for who the murderer is going to target. Naturally, while the two are in the police station, Nanako is kidnapped by the murderer, who is quickly identified as somebody who is quite evidently not Dojima's nephew. And Even Worse one of the options you do get is the ability to come clean and tell Dojima about your ability to go into the world behind the TV. He quite naturally doesn't believe you, and in fact becomes even more suspicious now that you have, in his mind, confirmed that you are lying to him. Too bad there isn't a TV right there in the room that the MC could walk over to and, I don't know, just stick his hand into to prove beyond a shadow of a doubt that he is telling the truth about the murders. Oh. Wait. There freaking is!
Another instance, admittedly retrospective: Taro Namatame has been kidnapping people throughout the entire game and throwing them into the Television, as he believes that this will keep them safe from someone trying to kill them. You'd Expect that he would do some sort of reconnaissance as to this new place, as even a cursory glance will reveal that it is infested with monsters and generally not a happy place. Or at least that he'd check up on the people he kidnapped. Instead, he just chucks them in there and does nothing else, meaning that your party has to go in and rescue them. Admittedly, the first victim he personally throws in is also the first victim you manage to save, so as far as he knows he really is saving them this way — but it's a complete coincidence, and had this coincidence not come to pass, he'd have been personally and primarily responsible for Yukiko's death.
Yosuke and Chie are stalking Kanji in order to get answers from him. Because they left the tree and their loud talking, he spotted them. To make a distraction, Yosuke claims that he and Chie are just two crazy lovebirds. You'd Expect Chie should know that Yosuke is not in love with her and goes along with him to get Kanji not to know they're following him. Instead she just denies this. It doesn't take a while for them to run away, leading Kanji to discover that they're following him. And then there was a wacky chase scene. ("NOOO COME BACK I LOVE GIIIIRLS!!")
Speaking of Yosuke and Chie; earlier on, he borrowed her "Trial of the Dragon" DVD. He accidentally broke it. You'd Expect knowing fully well that she has a short temper with him, Yosuke has to remain calm and give it to Chie without saying he did something to it, then walk away calmly afterwards. Instead he just give her the DVD in a panic and tries to run away. It doesn't take a while for her to pursue him and give him a critical hit to the nads.
In the Amagi Inn, the girls are enjoying the hot springs. Suddenly, Teddie cannonballs on to them as the boys show up. The girls get pissed off, thinking they're acting like perverts and start throwing buckets at them. By the time they left, Yukiko realizes she mixed up the schedule. (More of a "What a dick" moment). You'd Expect the girls should give the boys the chance, considering it's their turn. Instead they just keep this quiet to themselves, and not give them the chance. They don't even apologize for the misunderstanding.
Another one in the Amagi Inn: the boys planned to sleep with the girls as revenge for what happened at the hot springs. Earlier on, they found out that Yukiko has talismans on their room, which explains of their misery over the events of their stay. You'd Expect they do a sweep of the room, searching for additional talismans and checking to see if the room they got into is where the girls are sleeping at. Instead they just sneak into a dark room & as soon as the lights are turned on, it's Hanako and Ms. Kashiwagi! In other words, they got the wrong room.
Yet another one in the Amagi Inn (You see a pattern here?): So, the boys got kicked out of the Hot Spring even though it was their turn. You'd Expect the boys to report the incident to the staff at the Amagi Inn. Instead, the boys try to get back at the girls by sneaking in their room, causing more hillarity to ensue.
Naoto comes up with a plan to catch the killer: she noticed that the victims tend to be people who appear on TV specials, so she agrees to an interview in order to bait the culprit into targeting her. You'd Expect that she install cameras and keep her gun with her in order to be able to defeat the culprit or at least catch his face. Instead she doesn't do anything in preparation for her showdown with a serial kidnapper/murderer, and when the culprit rings her doorbell, he has no more problem kidnapping her than he had the others. Her plan turns out to be completely pointless and does not reveal anything about the killer's identity.
Chie, after running ahead in Yukiko's castle, has to be saved from her murderous Shadow Self after denying it. After she gains her Persona, Teddie tries to help them see the sense of going back for now by saying that since the shadows attack when the fog lifts, Yukiko isn't in any serious danger. You'd Expect first of all, for this to not even happen, but that aside, for everyone involved to realize that that is complete and utter bullshit given what literally just happened to Chie. She is proof that when your shadow self emerges, you are in grave danger no matter what the weather's like, as it was sunny that day. Even Worse, you would think that would make them even more hasty to get Yukiko out that very day, as they have already seen Yukiko's shadow self on the television. Instead nobody sees anything at all wrong with this plan. Granted, this is probably the only thing the designers could think of to excuse the game mechanic of allowing a given amount of time for individuals to be rescued—but that's still sloppy.