Dear lord.... the anime definitely doesn't do the game justice. I highly suggest you get hold of the PSP: The Best version of Dangan Ronpa and download the fanmade English patch and play it.
The anime is trying too hard to be like the game, when it simply cannot
be. I agree that the "Evidence found" and stuff like that just seem goofy and detract from the flow.
I think the thing I'm most bothered about is the fact that people who watch the anime before playing the game basically make it impossible for them to fully enjoy the game like I and many others have.
The animation is pretty nice but also seems to take a dive sometimes. The character art doesn't seem consistent enough for my liking either. (Whereas in the game it was pretty consistent and just... better in general.)
Lack of characterisation is a shame too, plot armor is quite an obvious thing.
I feel like I'm complaining too much but I was SO STOKED for the anime and it's just been a little bit of a let down. I will definitely be making another Dangan Ronpa AMV when it's finished airing though, purely for the 1080p footage ya'know.