ICOT:
I think this is a great topic. Often, frum Jews superficially say, “of course I approve of capital punishment; after all, the Torah allows it.” However, the issues are far more complicated than that. Do we apply the Torah standard? The Sheva Mitzvos standard? The expediency power of Beis Din standard (see Choshen Mishpat, siman 2)? Its not clear what standard American law should follow, or what standard we, as individual Torah observant Jews should personally approve of, or what standard we should advocate American governments to follow? (There are also more complicated questions about how we should view the U.S. federal system from a Torah perspective; should it be one size fits all, or should different local governments have leeway to control their own capital punishment? Also, how should we view the Constitutional Law on this issue from a Torah perspective; should Constitutional Law be given greater weight, or is it some kind of immutable inflexible Torah based standard all the way – even for non-Jewish governments?).
Leaving the Torah issues aside for a moment, its worthwhile to separate the question into several parts: (1) Are there any crimes for which perpetrators ought to be killed? If so, what are they, and what principle can we use to distinguish between them? (2) Assuming there are times when the death penalty is appropriate in principle, can we ever be sure that the convicted defendant in fact committed the crime? (3) If not, can we rightfully execute him anyway since he had the benefit of a fair trial?
A very complicated issue. Just some ideas of how to think about it, without coming out one way or another.