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In Persona 4 the characters refuse to tell the cops about the tiny bit about the murders taking place inside a TV because "They would be suspicious" (what?). When someone who is trained in investigating crimes finds out, major progress is made. The fact that Man Behind the Man is with the police doesn't excuse it when the characters have no idea at any point.
Near the end of the game a character refuses to believe the idea about the TV world and has you taken to the police station. The problem is there is a TV right in front of you during this scene, and a TV in the room you are taken to, but you never get the option to show it.
Even worse than that is the fact that the protagonist has just received a letter from an unknown person threatening his family if he continues to interfere. However instead of taking Nanako with them or making sure that someone stays with her Dojima simply leaves her on her own. What happens next is both easily predictable and would have been avoided if either he or the protagonist had actually been using their brains.
Both Persona 3 and Persona 4 have another issue that mars otherwise flawless localizations: the ending songs, which are sung, are not translated in any way, even through subtitles. Why is this a wall-banger? Well:
In Persona 3, the ending song is a really important plot point in that it's meant to be Aigis singing to the dying Protagonist about how she'll always remember him (and deep down even wants to find a way to save him), and it drives the point that he really does die. It can be much harder to understand the ending if you can't understand the song, and even worse, if you don't understand the song and thus Aigis' feelings at the end, parts of The Answer can come across as nearly nonsensical - and did at first for many Western fans who didn't know what The Journey's end song meant at first.
Persona 4's situation is thankfully not quite as dire as the one above; the ending song just amplifies the Crowning Moment of Heartwarming and Tear Jerker aspects of the good endings. The ending does lose a little punch if you can't understand the song, though, and its message of continuing to love and stay bonded to people no matter how much time and distance may separate them, and how without them you can't find that which you once lost - that is, the truth.
Possibly a problem of the plot requiring to do so, but the fact that the party in Persona 4 seems to catch on after two or three instances that yelling "You're not me!" causes the Shadow to go berserk and attack them. You'd think they'd tell people to not flat out reject the Shadow if they don't want to be attacked, but they don't. Eventually, as the game goes on, the party does lampshade this and says they can't really be bothered, since the Shadow's opposite is just gonna say it anyway.
During the hospital scene in the fourth game, where they confront Namatame, Yu should logically be the one most up in arms against him and lost in blind hate. Instead he is the sole member who manages to remain calm and see something is wrong and even call out the others when the only one who really should have been able to do that would have been Naoto who is both a professional and has known Nanako the least amount of time.