Avi K,
The Rambam is explicitly not talking about a bais din. The torah already says that a person shall be put to death only on the testimony of 2 witnesses, see the Ramban on the sefer hamitzvohs. The Rambam is talking about a case where its not bais din, such as Dovid. And Dovid killed not on circumstantial evidence but on an admission which is 100%. The gemora says that a Ben Noach is put to death on the testimony of one witness, and this is because he is testifying that he is 100% sure.
How can you possibly allow putting a person to death if you are not certain that he is guilty.
As to Bush, the man’s name was Gary Graham, and he did this while he was running for president which shows that he understood that people in America would not at all be troubled with his refusal to simply allow the new evidence to be heard. The reason that it was up to Bush was that the courts did not hear this evidence and so there was no basis for an appeal. The only way to save him was if these witnesses were allowed to be heard and this required a new trial. So it was up to Bush to use his power as governor to order a new trial.
Under the law you cannot appeal a jury verdict. That is the jury decides questions of fact and you cannot appeal their finding of the facts, even of the whole world thinks they were wrong.
The only basis for an appeal is if there was a legal mistake in the trial, such as certain evidence should not have been admitted, or that new evidence was discovered that was not known of by either side after the trial. And even if new evidence is discovered there is a time limit, which varies based on jurisdiction, as to how long after the trial it may be the basis for an appeal. That is if there is clear evidence that he was not guilty that came up 8 years later he cannot appeal based on that.
A court case is also a game. For example if the defense knew of a witness, or 5 witnesses but failed to ask them to testify, its too late and the man on death row cannot appeal that these are 5 witnesses that say that he didn’t do it.
As to the supreme court they have held that “actual innocence”, that is that there was no problem with anything the court did but that he claims that he was in fact innocent, is not a grounds for appeal.They allowed a man in Georgia to die recently despite the fact that every single witness recanted and said that the police threatened them that they will arrest them for crimes they committed.
The supreme court also held in a case in Alaska that a prisoner does not have the right to demand to get access to the DNA evidence that is in the possession of the state.
As for rooting out prosecutorial misconduct the supreme court recently sent a very strong message to prosecutors who are contemplating withholding evidence. An innocent man that sat in prison for 22 years till he was exonerated due to prosecutorial misconduct sued that prosecutor for the 22 years of his life that he lost. The court ruled that as a government official he has immunity and cannot be sued. So the court sent a message to every prosecutor that you will get away with it.
So if you want to address a philosophical question about capital punishment you should describe exactly how this punishment will be decided on. In America when people speak of capital punishment they are referring to the capital punishment that the courts order.
PS I went to Law School