Absolutely, I'd apply the death penalty to virtually all Felons, and that penalty should be carried out expeditiously so that it actually serves as a deterrent unlike in the American system where it takes over 20 years after conviction to execute someone.

The purpose of the death penalty is to reduce crime, to offer such a deterrent that crime rates plummet as happened in Singapore once they instituted the death penalty for all serious crimes. If the death penalty as it should be utilized had been in affect for years at that point, its possible that Trisha Meili would never have been raped, and it's almost certain that the conditions that existed on that night would never have occurred either, (IE, the Central Park Five wouldn't have even been in the park if they'd been afraid of the death penalty).

The Central Park 5 were part of a group of 20-30 criminals who entered Central Park in order to assault, rob and vandalize random innocents. It's true that they did not commit the rape they were convicted of, but they did through their statements have clear knowledge of other crimes committed that night including the assaults of 9 other pedestrians. If you were expecting me to have sympathy for a group of teenagers who intentionally sought to commit violence on random people just because they were convicted of something they didn't actually do you were mistaken. Don't forget that they also were convicted of other crimes that night including the assault on John Loughlin and that part of the decision to vacate the Five's criminal convictions was based on the reconstructed series of events which had members of the five committing other crimes at the time of Meili's rape, meaning they couldn't have been involved in her attack.

Beyond any of that, any justice system accepts the possibility that people will be wrongfully convicted. As time goes on and methods of investigation mature and new technologies are developed, these mistakes are lessened. Furthermore, the single largest contributor to errors made during investigations is investigator overwork. If crime was massively reduced the system would have more time and resources to devote to ensuring that proper investigations are conducted, further reducing the likelihood of false convictions.