I have to disagree, the first priority should be to not overstep their boundaries. In this case that would be to not punish the innocent, and then to prosecute the guilty.
Now you see why I'm cynical of government.
People can be proven guilty, confession, DNA eidence, eye-witness testimony, etc. It's hard, but it has to be.
I firmly belive that if you start framing a justice system by asking yourself "How many innocents are we willing to punish to ensure we punish wrongdoers?" You've already failed. If you absolutly must have a question like that ask "How many criminals are we willing to let go to ensure that no innocent is unjustly punished?"
So would you be in favor of government surveillance?