These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Base Breaker: Ayase. Some love her for her shamelessness in being frank, others hate her for it.
Demonic Spiders: Grimies, purposely placed where they are in the final dungeon to make you risk the 40 minutes it takes to actually reach the final boss in one fell swoop. They are also The Unintelligible, which means that they're hard to negotiate with.
Any demon capable of spamming multi target ailment attacks like sleep and guilt, such as Nightmares and Arpachis. Imagine being powerless and mesmerized to attack each other.
The above is remedied by equipping personae which reflect or null their magics, but the trope is still upheld due to the rarity of those personae, plus the need to move onto better, more capable personae.
Kuchisake-Onna is extremely hazardous against those who do an SQQ max Ambrosia run, in which the gamer at level 20 has to go into Thanatos Tower first. In there, she's commonly fought, she can't be talked away (easily), and she spams Mamudo, which will most likely off any member not fortunate enough to have a dark type persona, which at that point in the game, is extremely limited.
The toilet demons!
Ensemble Darkhorse: Eriko surprisingly. It does compute that she's a playable in Persona 2: Eternal Punishment.
Brown, and to a smaller extent, Mark, tend to get a lot of love from fans too. Mark probably because he dances crazy.
Fridge Horror: Avidya World. It looks like your typical final boss dungeon, with creepy music and dark, distorted halls. But if you look at the doors closely enough, you'll notice that Avidya World is a twisted version of your school. And nearly all the doors of the "normal" school refuse to budge now...
First Installment Wins: Averted/inverted. The original Persona game is easily the worst of the lot, with clunky mechanics and obtuse fighting systems. Indeed, the series has evolved nicely since then, with Persona 2 being a cult hit and Persona 3 being a total smash hit.
It does have an incredibly diehard fanbase though, mostly made up of fans of the PSX version. Some fans see it and IS/EP being truer to the idea of what a "Persona" is.
Seinfeld Is Unfunny: This game has not aged very well, and a lot of the criticisms for it were this.
Unfortunate Implications: Takahisa in the NA version of the game is called Guido, which is a a derogatory slang used against Italian Americans. It also didn't help matters that the character's 2nd form in his boss fight is called Super Guido. The name issue was remedied in the next game by having the Guido name used as an alias.
Woolseyism: The PSP script compared to the original North American release. Atlus' NA localization team goes to great lengths to grasp every last nuance of characterization and mythology.