Please don't throw around Gödel's Theorem before you've really understood it— that's one thing that makes people look like cranks!

"When does that ever happen and how does answering that question help me be more ethical?"

Very rarely; but pondering such hypotheticals has helped me to see what some of my actual moral intuitions are, once they are stripped of rationalizations (and chances to dodge the question). From that point on, I can reflect on them more effectively.