Lighter,

The off-hand tone of "Even if we make a mistake sometimes" suggests that people generally don't think or care much about the "mistakes." They're too busy with their own problems.

Not quite as I understand it. The irony lies in the fact that ideology insist on its truth in spite of obvious contradictions. More bluntly: "Murderers deserve their death penalty even if they are innocent." This is called "dialectics" (or "doublethink"); Jason may know even more about it than Pete Seegers did.