There wasn't much of a benefit to replaying the game, at least not yet. I only got about 75% of the way through for my second time, so I didn't get a crack at the alternate endings, but I knew that was a strong possibility going in. There was some foreshadowing that I didn't notice the first time through, but that mostly made me feel like kind of a shitty person for not picking up on it earlier (you help a couple of your classmates get married, and they subsequently shun you afterwards - I previously thought it was because of all my delinquent antics, but it turns out that they were not happy about Brigton's tradition of state-sanctioned wedding-night rape).
In trying to sum up my feelings for Dangerous High School Girls In Trouble! as a whole, I can't get past a sense of being deeply divided about this game. On the one hand, the story and characters are pretty great, but then the final act's use of rape as entertainment, while thematically appropriate, is kind of troubling. The minigames are mostly awful, but I wound up getting used to them after awhile. Exploring the game's world was interesting, but there were a few too many times when it wasn't clear what I was supposed to do next.
Overall, I'd say that it makes you work just a little too hard to get to the good stuff. If you stick it out, it has a lot to recommend to it, but the early game, especially, is a drag, and if you quit an hour or two in, that is both completely understandable and cheating yourself out of the best part of the game (which is, of course, the Donkey Mayor storyline).
I don't think Dangerous High School Girls In Trouble! is going on my replay list any time soon. I love its attitude and sense of style, but it benefits not one bit from being a game. I think the story would work better as a comic or a heavily stylized movie or a radio play. The interactive elements are mostly just a way to kill time.
So, I don't know. It's good to have these quirky little corner-case games that maybe don't fit the traditional mold of what makes a "good" game, but nonetheless manage to do something different. And while there were times I wasn't eager to play it, I enjoyed myself more often than not. I guess "moderate enjoyment" + "novelty" is actually a pretty strong combination.
It's worth playing at least once, but don't make the same mistake I did - create a separate save when you go to confront Jimmy Finn. That way you don't have to replay the whole game to get all the endings.