I just finished uploading Case 1 of Phoenix Wright 3. It's a pretty exciting case. In fact, it's much more exciting than a tutorial has any right to be. Usually a tutorial is an easy segment that doesn't have anything to do with the real game; all it does is set up the game mechanics. But in this game, the tutorial is one of the important cases, plot-wise.
I also like this case, because Mia Fey steps up and fulfills her role as the major lawyer-heroine of the series. She is a good character, and it's a shame she doesn't take the spotlight more often. In fact, most of the time, she gets treated as gratuitous eye candy who doesn't really affect the plot. (See Case 3 of this game for an example of this).
The commenters on the video walkthrough say they like how the game references the Harlem Shake. I think that's a popular dance or something. Since the game came out in 2007, I doubt that the reference is intentional. People seem to enjoy it anyway.
It's also an interesting case, because it sets up how Phoenix Wright first met Mia Fey, five years ago. The college version of Phoenix Wright is completely different from the lawyer version we're used to seeing. In college, he was sort of a crybaby who wore an ugly pink sweater all the time. It's interesting to see a completely different side of the main character of the series, even if it's a less-than-impressive view.