Problems with the Death Penalty

I just listened to a news story about someone in Georgia who has had significant doubts raised about his guilt. The only person speaking on camera in favor of carrying through the death penalty was the mother of the slain officer. She said that it should proceed and she wanted to ask those who questioned it how many of them had their sons shot. What difference does that make? Likely kill an innocent man because your son was shot? Are people really this stupid? I am in favor of the death penalty when it is properly applied, but I find that our modern legal system allows the rich to buy their way out of it and the poor to get railroaded. That is flawed. We must protect society, from cruel predators in society and inside prosecuting offices.