I'd like to start by saying that I really love the idea behind this crossover. I've always taken a liking to darker stories set within the Pokemon universe, and Dangan Ronpa is one of my favorite visual novel series. After playing this game for a little while, it's clear that a lot of thought went into the story and characters, and it's not just a retelling of the first DR game with Pokemon shoehorned in as I expected.
However, there are a few things which really hold this game back from its true potential. For a Pokemon game, there isn't a whole lot of battling - which is not inherently bad, I'd play a visual novel with Pokemon in it even if you never get to battle - but from what I can tell, only the final boss fight is mandatory, and the game gives you a Pokemon for that, so there's no point in fighting any of the optional battles or doing any training. One could argue that it helps if you really suck at the trial segments, but... since the game puts you against a wild Pokemon if you fail, you can always run. And so far I've never failed to escape one of those fights with my untrained level 15 ditto. So, there's essentially no consequence for getting a question/prompt incorrect, and thus no reason to investigate when a murder takes place. Overall, that's about 80% of the gameplay rendered more or less totally pointless.
As for the story and characters... the story is good. It's fairly well paced and did a decent job at keeping me interested (which, knowing myself, is saying a lot), there were plenty of clever ideas and the Pokemon were integrated well. The characters seemed distinct and interesting enough, but I found it hard to get attached to any of them... which I'm going to attribute mostly to the face graphics. I'm familiar with the avatar creator used to make them, I used to use it a lot myself when tinkering with RPG maker and the like long ago, but the problem with it is that the faces produced usually end up looking very similar. The characters in Distrust all blended together for me as a result. (The Japanese names didn't help, but I had the same problem with DR itself when I was first getting into it, which is more the fault of coming from a different language than anything. Still, since this is taking place in the Pokemon universe and some of its existing characters are mentioned, it might have been best to stick with more English-sounding names in my opinion.)
Anyway. What I'm wondering is, since you have custom art for a lot of the scenes in the game (deaths, smooches, etc) why not do the same with the faces so that each character has a more distinct, easily recognizable design? This is one of the things that made DR's characters so memorable; every single pose and expression was unique and fit the character and the emotion they were trying to convey, and they all had very distinct designs to the point where you could identify a character just from its silhouette. I'm not saying you have to make 20 different full-body poses for every character, but something along those lines would really help them stand out.
Onto the next issue: the bugs. The game breaks constantly and it's too easy for a player to get themselves totally stuck through no fault of their own. The game feels really cobbled together, and this became exceedingly obvious when I looked at the game through RMXP. Don't get me wrong, I'm actually very impressed that you managed to create such a coherent experience with so little organization and tact. It's a work of art, really - reminds me a lot of the game projects my brother and I used to tinker around with when we were younger, where we'd basically mash things together until they worked... well enough for us to move on, anyway. Except, unlike us, you had the fortitude to carry the project to completion. I have to give you massive props for that.