Death Penalty
This is a tough one. First of all I don't like the thought of someone being put to death even if they committed a crime. However, my first reaction to such a person (after hearing about the awful crime) is "that person deserves to die", which is a normal human reaction. After some thought, I tend to change my mind, and think that even a hard core murderer could still obtain salvation.
However, while it is obvious my own opinion on this subject is torn, I don't think the scriptures are torn on the issue at all. We know that under the Law of Moses, the death penalty was required for many infractions. However, as Christians we are no longer under law, but under grace. What is said about the death penalty before the law? In Genesis, after the flood, God makes a statement about those who shed blood:
Genesis 9:6 Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man.
This is one of the first commandments given by God, and it is clear his intention was to give man the governing authority to execute this punishment. It predates the Law of Moses by many years, and was given to all mankind.
Has this ever been refuted or retracted? Not as far as I can tell. However, does this mean that anyone who kills (murder only, this does not apply to accidents, self defense, etc.) should be put to death? I think it means they can be put to death (by the government). However does it mean they have to be put to death? Taken by itself, this commandment would seem to leave no room for mercy, however, we can't base our doctrine or beliefs on just one verse. We have to take the entire scripture. And if you have read the Bible you know that mercy is often shown as a desirable virtue for us to have. Forgiveness and Mercy would (in my opinion) allow us to forgo the death penalty, though execution of an unrepentant murderer is easier on our conscious.
What I just said about mercy is fine for individuals, but it is not individuals who are given authority to execute someone, it is the government which does this. The governments of all nations are given divine authority to govern, and this includes the use of the death penalty. As individuals, we are free to show mercy. Nations can also show mercy, but if they do not, I don't think it is a national sin to execute someone (unless the person was not guilty, or guilty of something less than heinous).
The death penalty (as given in Genesis 9) was only for murder. This predates the Law, but more was said about it under the Law as given to Moses. Though we are not under the law of Moses, we can certainly refer to it for examples, and it clearly distinguishes between first degree murder (pre-meditated) and other forms of murder (crimes of passion) and self defense, and accidental killings (manslaughter). We can use that as an example.
So the bottom line is that the scriptures authorize the use of the death penalty by Government. I don't believe that this allowance extends to individuals executing someone (i.e. a lynch mob or personal vengeance), even if for murder. Only the Government has this authority. The scriptures also make exceptions. Remember Cain who murdered his own brother Abel? God allowed him to live, though in exile. Consider this. That means mercy is often preferable if possible.
One thing that should not be overlooked, is that the murderer, even if guilty of first degree murder, is still a human being. He/she can be saved by accepting Christ. They might have their soul saved by believing the gospel, even though the Government might still put them to death for their crimes. This is sad when it happens, but it is good that the person is saved from hell. We will be with them in Heaven someday. It is more sad when a lost person dies (by whatever means), for the Lord does not want anyone to be lost.