Something I think goes underappreciated about Persona 4 is the way that it gives you all the tools you need to solve its greatest mysteries if you put the time in to explore. There are special NPC interactions throughout the year with plot relevant characters like the Moel Gas Station attendant, Mitsuo Kubo, and Namatame that give insights to their roles in the story.
Take the attendant, for example:
This character ONLY appears on rainy days. Persona 4 teaches you that rainy days are important. The Midnight Channel, your rescue deadlines, all of it links back to rain, so if you go to the gas station on those days, you get dialogue. This NPC is never available on any other day. So, if you catch onto this pattern, the gas station attendant becomes more significant than if you never explore the town on rainy days and just focus on your story objectives, Social Links, etc.
But it's not just the gas station attendant. This applies to other plot significant characters, too.
Taro Namatame is a special NPC who only appears around set dates in the game's calendar, but one who appears throughout the entire story. The game teaches you he's important by giving him a portrait. Portrait characters are always going to be more meaningful, which actually makes the gas station attendant a fascinating subversion by having a distinct design and even a voice actor in his introduction, but not a portrait until the game's final day.
But if you interact with Namatame, you will get insight to his feelings and get early evidence that he did not kill Saki or Mayumi Yamano. If you explore, if you investigate, you will have the tools you need months in advance to confront the game's red herrings and see through the fog.
But you have to put in the effort. You have to commit yourself to the investigation and leave no stone unturned. Persona 4 embraces the mystery genre even in its game design by encouraging exploration and interaction with Inaba itself.
Mitsuo is another example. He's introduced earlier with a portrait and appears on the overworld for a few months before he becomes plot relevant. During this time, you do get glimmers of... possible concern intermixed with his less pleasant personality.
But he genuinely is furious at the police for their inability to catch the killer. He may not be nice, he may look creepy, and he may be a copycat killer who wants the attention, but with his dungeon painting this action as a result of social ostracization, expulsion, and possibly even neglect, he becomes a much more layered, if ultimately still antagonistic character. For more on that, I recommend this tumblr post. So, once again, you are given a hint that he's a red herring, if you pay attention, remember those interactions, and ruminate on them.
There are other really cool NPC interactions that update throughout the game, like the shopkeepers, but I bring these examples up specifically because they demonstrate how Persona 4's game design sets you up with all the tools you need to solve the case that I think go underdiscussed.