How, exactly, do you tell the wrong answers from the right?

I've been writing programs for almost 50 years now, and I've always been baffled by how many gross bugs other people's programs have. However, I have always thought of myself as an engineer, where I need to prove to myself that my program works completely, beyond reasonable doubt.

So do I want the fast glass of milk that might have some turd in it, or the slower glass with none?