murder by definition -- not in legal sense but in the sense of what the word is -- is the unlawful killing of one human being by another. in this sense a solider does not murder when he is involved in war against a belligerent. i don't know why you want to godwin this but in that case it was against the laws of war so it was indeed unlawful. it also WAS against German law, in that no German law supported it other than the Reichtag Fire Decree which gave Hitler's orders as much weight as law but that doesn't mean the law was actually changed (and frankly the Reichtag Fire Decree was itself unconstitutional so... it was all illegal).
yes, the appeals process exists. in fact it is unlimited for people on death row. but that doesn't mean the guilt or innocence is being discussed again. the appeals do not find fact again. they look at what was found and if there was reason for a mistrial or something they find that. but they aren't deciding if someone is guilty or innocent. at most they will vacate a decision.
my point in separating them is that punishment is not related to whether someone is guilty or innocent. we as a society have decided that "guilt beyond a reasonable doubt" is our standard for determining guilt. so if someone is found guilty when they are truly innocent of the crime, that has to do with the finding of the guilt. that's where the problem lies. that the person is punished in some fashion is irrelevant to where the problem is