I know there is still support from the majority of the public over the death penalty, but thanks to advances in forensics that have exonerated many a person convicted of murder, including a few on death row, support is rapidly plummeting.
The fact that once an innocent person is executed for a crime he or she didn't commit and there is no way to right such a wrong is reason enough for the death penalty to no longer exist. Errors can be made, murder cases are especially prone to prosecutorial and police misconduct and faulty witnesses.
I know, I know. People like Christian Longo and Rodney Alcala take up too much oxygen and have no redeeming value to our society, but the death penalty isn't something you can just pick and choose who to have the state kill and who to spare.
Besides, the death penalty is completely arbitrary and tends to single out those who are poor or are minorities; in other words, people who have less access to good defense lawyers.