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.
Art-Style Dissonance: After 3 and 4, the series gets more brightly coloured, including quirky non-human sidekicks (Especially Teddie). However... the game is still not afraid to mention characters dying (in sometimes gruesome ways), show naked women, or even touch upon themes like impending death and apocalypse cults. In fact, the series has arguably been getting more graphic as it goes on, with Persona 3 and 4 being rated "M", whereas the first three only got a "T" rating. (The first also got a K-A rating, but that was a heavily Macekred version)
Broken Base: With the main series, due to its popularity overshadowing it and everything else Atlus makes. At this point, the base parallels the Law-Neutral-Chaos alignmemts: Law represents fans who hates P3/P4 fans and their Fan Dumb (though it borders on elitism, Chaos is P3/P4 fans, and Neutral are full of fans that sees the pros and cons and tries to embrace all games.
The fanbase itself has suffered its own breaks:
Some of the older fans prefer the more "Traditional" Persona 1 and 2, thinking instead that the games are a little more "True" to what a "Persona" is. Sometimes it's because of nostalgia, as they were the first Persona games they played. Other times, it's more because of some fundamental gameplay changes such as characters talking with demons, the taller characters who weren't as colourful, and everyone being able to change personae. The fact that Persona 3 and 4 don't really acknowledge Personas 1 and 2 very much doesn't help things either.
Some of the newer fans prefer the newer games, partly due to nostalgia, but also because they don't think that the first three games have aged very well. Other people simply like the feel of the latter two persona games, enjoying the Dating Sim elements as well as the increased character interaction and drama (Which wasn't as common in the first three.) Some may also feel the art of the first three (Especially Persona 2) falls into the Uncanny Valley.
Continuity Lockout: Averted - every game is essentially a standalone title. Even the references to the first Persona game in Persona 2 are explained. One can pick up "Persona 4" and not be lost. The only games this may have caused an issue are "Persona 2".
For some people, this actually didn't happen in Eternal Punishment, since Innocent Sin was not released outside of Japan until the PSP remake. The fact that there was a completely different adventure that had happened, leading up to the innocent sin actually intrigued a lot of North American players.
First Installment Wins: Averted - The first game was only a cult classic at best, and still to this day retains a cult classic.