The anime as a whole. Fans either call it a faithful adaptation with some extra plot thrown in, or they call it another example of the dark side of The Anime of the Game titles, where it butchers the story by cutting out all of the fluff that makes it worthwhile as a game, as well as having the obvious cases of Off Model and editing certain plotlines to make them less suspenseful or humorous.
Kanji's treatment in Episodes 7 and 8, specifically Yosuke and Narukami's reactions to Shadow Kanji as well as the the tent scene. Was it really funny or really homophobic?
Creepy Awesome: Ameno-Sagiri and Izanami. They were scary enough in the game, but general badassery the cast displays, Yu especially, and to see them, respectively, almost outright stomp Yu without his friends saving him, and bring him to his knees while barely lifting a finger makes them even more frightening.
Ensemble Darkhorse: Aika Nakamura, a side character introduced in the anime, saw a sudden spike in popularity after a scene in episode 6 where she stoically delivers Chinese takeout to Chiein the middle of a chase sequence.
"Funny Aneurysm" Moment: In Episode 22, after Yosuke gets' emotional, Yu, jokingly, tells him it's okay to cry. Yosuke flips out and yells "it's not like I'm a girl!" Just another wacky comedy moment, right? Come the start of the next episode and Yosuke is the first to cry at Nanako's death and naturally everyone thinks this is okay.
The rendition of the fight against Shadow Kanji in Episode 7. Were Yosuke and Yu homophobic and hateful assholes, or did they just not know how to handle such a situation? Was the scene supposed to be making fun of homosexuality, or making fun of Yu and Yosuke's fear of it? Another point of contention is that it was treated much less seriously than the other bosses, with the boys jokingly trying to leave Kanji to his shadow (compare to the game, where Yosuke still doesn't want to go in but puts that aside out of concern for Kanji).
The main character being renamed Yu Narukami in the anime (when he was known to some fans by his manga name of Souji Seta). Never mind that Yu Narukami was the canon name chosen by Atlus and the other was only made up for the manga, his canon name came second so therefore it sucks!
Signature Scene: The Investigation Team putting on their glasses against a stark yellow background in the second opening.