To me, the standard conversations have largely started feeling like the same shallow crap you get from start to finish.
Free time is a novel idea at first, but I don't think putting so much of each character's backstory within that construct is a good idea.
I think it's a by-product of them having so many characters in the game. They expect the player to do an entirely different mode, one with no investigations at all, in order to learn about all of them to any really appreciable degree.
It's too spread out overall - too many characters, not enough opportunities to get to know them better so you actually feel something more than, "Great, that person died, one less jackass who won't shut up." when they get killed or executed.
You get a portion of backstory when it comes down to the very end of each trial, but that's a lot of effort for not nearly enough payoff from a character standpoint.
Beyond that, you've got the gift giving thing, which doesn't feel right at all, really.
My character is in an insane situation, with life and death stakes, and I have to picture them shoving bear coins into a gambling machine in the hopes of getting that one item that'll make someone spill their guts if I give it to them. That's ridiculous.
The issues I have with the detective sections would be that they feel so long in 2 that they start to drag, the truth bullet system ends up being an unnecessarily contrived form of communication and debate, the two new mini-games they included don't mesh well with any sort of tension that should be present given the situation.
(Hangman's Gambit is better in a way, but it was pretty much a joke in 1, so the bar for success wasn't very high.)
I told them about the first murder in 2.
As for the ridiculousness factor, it presents the idea that every killer is/was a latent criminal mastermind, only they deal in absurd Rube Goldberg-style scenarios for committing murders.
There isn't a single death that makes me think it would happen in the real world. They just get more and more insanely elaborate as time goes on.
Almost forgot one other thing - the e-pet. If someone actually cared enough to maintain an e-pet in that situation, I would immediately consider them suspicious, since that would feel like an indicator that they're out of their frigging mind.
Total busywork padding, presented so you have currency for an ineffective, silly gameplay mechanic.