Seeing that you said the Law of Moses does not apply to Gentles [see What Does the Bible Say About Gentile Christians Keeping the Law of Moses?, is the death penalty wrong? If it is not wrong, who can be executed? Children? Mentally handicapped?
Answer
Your question seems to imply that capital punishment originated in the Law of Moses. If it could be found only there, then your question would be valid. The concept of capital punishment ordained by God precedes the Law of Moses, however. It goes back at least to Noah. "And surely your blood of your lives will I require; at the hand of every beast will I require it, and at the hand of man; at the hand of every man's brother will I require the life of man. Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man." (Genesis 9:5-6)
Although the New Testament doesn't specifically mention capital punishment, it implies that it is a power that governments can use. "For rulers are not a terror to good works, but to the evil. Wilt thou then not be afraid of the power? do that which is good, and thou shalt have praise of the same: For he is the minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil." (Romans 13:3-4) "The sword" Paul refers to is probably more than just common legal action. It is the actual use of the sword to execute justice.
As to the limits of capital punishment, that is up to the established governments. There is no scripture limiting capital punishment for murder. On the other hand, many countries consider execution of children (and the maximum age varies) and mentally incompetent to be unnecessarily harsh. But then, many countries also don't use the death penalty at all.