You can't design a system that is mistake free, but that can't be the basis for a abandoning a punishment/deterrence system altogether.
At some point you have to trust that you've implemented reasonable safeguards and that you've minimized the chances for wrongful conviction. After that, you can console yourself by recognizing that most wrongful convictions happen to bad people, not to completely innocent, law-abiding people.
"Well, it is one thing for Bill Clinton to say, I feel your pain. It is another thing for Barack Obama to say I feel your pain that I have caused." - George Will