We do need to fix our justice system so that we're not so quick to convict, and especially so that we're not so quick to intimidating people into agreeing to be punished without being convicted, but once someone is convicted, their experience (assuming they ever come out of the system) is such that they will not be willing to go back again. Criminals in jail should not be allowed any contact with other inmates. When they're not working at a prison job, they should be in solitary confinement. Drugs (tobacco, alcohol, and caffeine as well as the illegal ones) should be banned, and they should not have enough privacy to be able to effectively avoid the ban. (Guards who provide such substances should be sentenced to the same prison they cheated in.) Commercial entertainment should be banned too; they can have genuinely educational reading material or TV if they want.
Once a criminal has served his sentence, though, we need to be fair and actually allow them to rejoin society -- no job discrimination, no limited rights, no putting their convictions on public websites. If we can't safely let them out on those terms, then we didn't punish them properly; there certainly are those who we'd never actually trust to be our neighbors or working in our kids' schools -- but if we really can't trust them, we shouldn't let them walk the streets. Executing such people is not cruel and unusual punishment, it is rational and appropriate when the alternative is locking them up for the rest of their lives. Allow the condemned a choice of methods of execution. For every appeal or request for clemency that's denied, strike off the generally most pleasant method from the list. That should cut down on the level of complaint about lethal injection.