A rather obvious one if you're a die-hard Persona 4 fan, but the anime was announced on the same day the in-game story starts, and the character trailers show up the same day said character gets tossed into the Midnight Channel. Here's something interesting I've looked into: the anime (which started around the first week of October) runs for around 25-26 episodes. Now, following the trend of one episode per week, I've calculated that the anime ends around the same time the in-game story ends. Granted, the anime's going to probably be off around 3-5 days at best, but damn... talk about your Book Ends.
In episode 12 of the anime, Shadow Mitsuo's Lotus-Eater Machine seems to come out of absolutely nowhere and hijack the episode until The Reveal at the end. But think about it: Shadow Mitsuo has Evil Touch, an attack capable of causing the Fear status.
In the same spirit, Shadow Naoto's ray turns Yu, Yosuke and Teddie into old people. At the end of the episode, Teddie undoes this by using Energy Shower, referencing the game where Shadow Naoto often causes Exhaustion.
Drunk Adachi in episode 17 of the anime is hilarious. And then, if you know the plot of the game, it occurs to you that he's the one responsible for Naoto ending up in the TV in the first place, in part after the two apparently were in an argument about the case. He's so drunk because he's probably depressed that he didn't succeed in killing her.
How is it that Yu is able to defeat so many foes in the anime all by himself? Because his levels are through the roof: at the end of the show, he's able to summon a level 93 Persona, Lucifer, and use a level 96 skill, Repel Light. He must be going into the TV World to grind when no one's looking...
Hell, he already summoned freakin' Pyro Jack against Shadow Chie and Shadow Yukiko. That's level 32 against level 6 and 13.
This is almost canon. Remember the flashes of terrible things at the very beginning of the anime, with Youske shouting Yu's name? This most likely coincides with the Bad Ending of the game, where if you have no girlfriend, Youske calls you screaming that people are turning into shadows. Therefore, the anime is a New Game Plus taking place after a socially inept Yu threw Namatame into the TV, after spending no time upping his social stats (and therefore having no girlfriend). He starts the anime with a huge level bump, which is why he can summon insanely powerful Personas for the point in the story he's at, and also why his social skills are still inept. Fridge Brilliance indeed.
In the anime, Yu serves omelets to everyone, and then later reveals that he put wasabi in one of them. When someone asks who got the spicy one and nobody says anything, Yu says "Maybe they didn't notice." Who got the wasabi? Rise, who has a habit of cooking food that is spicy enough to knock out someone.
It literally did not hit me until the other day, but the protagonist's name in the anime (and most adaptations, save the manga) is "Yuu".
In episode 26 of the anime, Yu is confronted by an image of his own Shadow. His shadow reveals that, despite Yu's stoic and snarky demeanor, he is (as proven during the Shadow Mitsuo fight) very dependant on his friends and deadly afraid of losing them, to the point that he'd rather live in Izanami's world of lies if he could be with them. Yu agrees without a second thought. It makes sense since he is the only one from the group that got his Persona from the get go. This means that he was already aware and accepting of his own flaws and insecurities.
That, and he's done this so many times to know the consequences if he were to reject them.
It goes even further than that. Despite being so chill and in control of his emotions, we never hear anything about Yu's personal life. In fact, he seems absolutely remiss to even go back. Why is it his life in Inaba seems to matter so much more than the life he had before? He didn't have one. He was miserable and alone; what the entire cast — and the audience — was led to believe was badass stoicism was desensitization from loneliness. Suddenly, the aspect of forming connections being a core gameplay mechanic become far more personal. Not only that, Yu's probably one of the people who would be most tempted to accept the illusion of the fog, giving his bravery in facing it far more consequence. Damn, one little additive in the adaption really turned things on their head...
Adachi's dungeon being a dark and distorted version of Inaba makes sense considering that one of his main flaws is believing that the real world isn't worth living in. However, it also serves a double meaning. Episode 24 of the anime takes care to point out several different location such as the Amagi Inn and Junes, both in a wrecked state. This doesn't just represent Adachi's reality, it represents what will happen if the Investigation Team doesn't stop him.
One step further, fellow troper: Adachi feels the world isn't worth living in, but why? Because he sees it as twisted and unfair. To this end, he uses the rest of the world as the excuse for everything he does. Now let's see, an exaggerated state of mind used to enforce a truth that the individual responsible for is unwilling to admit, where have we seen this so far...?