Yitz,
1. Rambam is talking about a bet din sitting as a regular (non-emergency) court. It does not apply to the secular authorities or a bet din using emergency powers. I refer you to my previous posts, which included references to Mishna Tora and the example of David HaMelech having the ger Amaleki summarily executed on his confession alone – which is inadmissible in a regular bet din proceeding.
2. The question of prosecutorial misconduct is a technical question, not a philosophical question – which is the topic of this thread. It certainly must be addressed in a manner that will root it out (as well as defense misconduct). I find it extremely strange that Bush refused to grant a new trial – and that the decision was his and not that of a court. I also find it extremely strange that the many appellate options, both to state and Federal courts, available were not used. On the Federal level (and I assume that the Boston Marathon case inspired this thread) the precautions are greater.The protocols for approving pursuit of the death penalty are quite rigorous (they appear on-line in the DOJ publication “The Federal Death Penalty System)and include the appointment of an experienced death penalty defender to the defense team IF the request for pursuing the death penalty is approved.