I've been hesitant to bring up this point because I don't want to appear to be prejudiced against people in prison, but this case that Suddenly mentions is too exemplary to ignore.
There really aren't very many innocents on death row. There are some, possibly too many, who are innocent of the crimes they were convicted for, but there's a pretty good chance that they are not nice people. Now I am not saying that because a person is a head case and violent that he deserves to die. I am saying that calling these persons "innocents" is... well... generous to a fault. It is rare, even in Texas, to send a person to death row who has no priors or no history of violence.
Usually when someone is sent to death row, it is because the crime is against someone who, to use popular parlance, didn't deserve it. Killing rival gang members or killing in a bar fight, or even killing a spouse's lover is not the sort of case where prosecutors seek the death penalty most of the time. Usually it is in cases with the proverbial "senseless killing". While it occasionally happens that a "senseless killer" is a person with no criminal history, such cases are as rare as white crows.
Does a person whose prior life of crime deserve to die simply because he is a bad person, rather than because he committed the crime of which he is charged? No. He does not. Thanks to people like Suddenly, they rarely do. Occasionally, but rarely. But is this same person truly deserving of the label of "innocent"? Well, we are all innocent in some ways and worldly in others. I'd say these guys are more worldly than most.
If errors are made, I prefer them to be made in favor of those who more truly deserve the adjective "innocent". Suddenly's example above shows that even if innocent of the crime with which they are charged, the defendants in such cases are often far removed from anything that we could reasonably call innocent in the general sense.