It should be obvious to the user that our quality is phenomenal. They'll have to fix it. The customer expects a perfect job from us. And any tiny defect can blow the reputation of the whole system, in the user's eyes. In addition, the team should have documented methods for design, defect prevention, and inline testing, and tools to mechanize these.
Most teams review designs, review source code, and test compiled code.
If this principle becomes part of our culture, each step can concentrate on preventing or removing its own defects, counting on clean input from the prior step. We need to learn from our mistakes, look for better ways, question authority. Our methods and processes have to keep evolving to meet changing conditions. I think a story like this will not only work as good advertising, it will also reduce development time, cost and risk.