@Crashman, "I already have."
I suppose you're referring to your assertion that it is impossible to follow Jesus and believe in capital punishment due to the story we find recorded in John 8:1-11. I have already responded in part by quoting Jesus as saying that he came to fulfill the law, not abolish it. Thus, the moral law of God is not to be abandoned completely. However, the laws that were given specifically to the Israelites are no longer applicable in every detail. We can still determine from them which sort of things are morally acceptable and which are not, but we are not required to legislate those things in our own government, much less to proscribe the same punishments. Israel was its own country with its own form of government and its own laws, just as modern countries each have their own. With this is mind, what do we see? The law requiring that an adulteress be stoned was a specific law given to the Israelites. (I'm sleepy at 10:30pm and can't find the exact reference; I believe it was in Leviticus or Numbers.) But the command to execute murderers, as I already referenced, was a general precept found in Genesis 9:6a, given to the remnant of the human race after the great flood. Thus, it applies to all who are descended from them, i.e., everyone. So it is certainly not easy to dismiss capital punishment as a dispensable command. And of course if Jesus is the same God who gave that command in Genesis, we cannot suppose that he would contradict himself.
In John, we do see Jesus removing the death penalty for adultery. To explain why he had that authority requires more of an exposition of Jewish/Christian theology.
Israel was the initial kingdom of God, his special people on earth who were supposed to obey and love him. The Jews looked forward to the coming of a Messiah (Jesus), as a political ruler who would free them from the various nations that oppressed them throughout history. Instead, he came as a spiritual ruler who would free them from the effects of sin. As a spiritual ruler of the Jews, then, he had the authority to abolish (or at least suspend) a part of the moral law. He did that for this case of adultery, but I do not find where he did that for murder.