That case is one of the ones I make a point to skip on re-playing. A lot of third cases seem to be that way since they're sandwiched between the cases that introduce characters, and the cases where the climax starts to roll around. With the exception of a few key events, like some development for the prosecutor, you could take them out and the games would be largely unchanged.
The later games, like the Investigations duo, Dual Destinies and Spirit of Justice, do a much better job of making the third case relevant and not just feel like boring filler... Although Spirit of Justice does that with its fourth case instead.