Assuming the students are guilty the police/prosecutors had a couple of chances to get them but they blew both of them. The first was in the interrogation. Although the interrogation was probably illegal, since they went ahead with it and used it in court anyway they should have at least gotten incriminating information out of it. If Amanda is truly guilty they should have been able to get her to say something only a participant in the crime would know. It's not enough you say Patrick did it, give us something more. Tell us about the staged break-in. Give us details we can corroborate. And most of all tape it. If you have Amanda on tape revealing intimate details of the crime verified in the forensic record, you're doing a lot better than getting her to allegedly regurgitate the very vague theory of the crime you're feeding her to repeat.
The second area where the prosecution dropped the ball was not cutting a deal with Rudy and getting him to testify against the students. As it stands now Rudy Guede is serving a semi-lengthy prison sentence, and Amanda is free. If she was the primary aggressor, I'm sure the family would consider it justice if Rudy would agree to give corroborating testimony against his accomplices in exchange for an even lighter sentence if it meant Amanda and Raffaele behind bars for decades.
Obviously Rudy's many stories, from sitting on the toilet, to having a date with Meredith while she complains about Amanda stealing from her, are absurd. He would have to tell the truth which would include his participation in the crime with Amanda and Raffaele. And he would have to be able to partially corroborate his story. For example, producing evidence showing how he and Amanda or Raffaele communicated or interacted prior to the murder. In addition, allowing the defense to cross examine him, and being able to hold up to that, would go a long way towards helping the prosecution prove what they set out to prove.
Instead Rudy seems to have been quietly whisked through the system. His abbreviated fast-track trial a footnote in the events. The absurd maneuvering to get his letter which made vague statements against the students into their court without the possibility of cross examination doesn't instill one with a sense of confidence in the prosecution's faith in Rudy as an accomplice with the students. Really it makes me think they don't have any faith in him at all, as if he doesn't really have any useful information for their case.
It seems like both the prosecution and the PGP are afraid to poke into where things went wrong, because such examination leads to more than just doubt in the prosecution's competence. I think there's a good reason the case rested on twisting sloppy forensic work into suspicious webs that didn't amount to anything, because it's all they had and they knew it. Mignini knew Rudy was just a burglar the second he popped up in their investigation. He put together the only case he could, and it was never going to be enough to sustain a conviction.