I'm replaying the first Phoenix Wright game right now, and I have to admit that there are problems with Case #3. Here are three glaring problems I found.
#1. The murder takes place at a TV studio, after a run-through and before a rehearsal. At the end of the first day of trial, the huge plot twist is that the director was there to oversee the rehearsal.
No, seriously. Up until this point, everyone took it for granted that no one besides the actors were there for rehearsal. True, the security team lied about who was at rehearsal, but that's still something our heroes should have questioned earlier.
#2. There is an automatic camera, which takes a picture whenever someone passes by the gate. The camera took a picture of the murderer, going to the crime scene. This photo is key evidence in the trial.
At the end of the second day of trial, Phoenix realizes that there is no picture of the victim going to the crime scene. Um...why didn't anyone question that earlier?
#3. The last major plot twist of the case is about the murder weapon. All along, everyone thought it was [Item X], when it was really [Item Y]. On the first day of the trial, you learn that [Item X] was broken, long before the murder took place.
No one questions this. Everyone knows [Item X] was broken, but they still think it's the murder weapon. That's a huge thing to overlook.
Case Four of the game also suffers a bit from this, with "the second photograph" and "the third bullet" that no one bothers to look into, until the second day of trial.