Capital punishment is an interesting question. I'm instinctively against it because it isn't state killing in the true sense, it's the judiciary paying a bloke who doesn't mind killing people he's never met for money, which is wrong on a number of levels.
However if the murder rate were to substantially fall based on its reinstitution, it would be very difficult to argue against it as a social good. The problem is although the murder rate has doubled since the abolition of the death penalty, other factors have to be taken into account for that increase, and by 2012 it was falling fairly dramatically from 2002 with over 1000 a year (172 attributable to Harold Shipman), to half that figure by 2012. Crime as a whole in England and Wales has fallen 40% since 1984 while the willingness to report crime has increased. The big increases are in knife crime which is not covered by the recall of capital punishment except for murder.