The key ideas in Freakonomics that challenge conventional thinking are centered around the concepts of incentives and how they drive behavior, as well as questioning the accuracy of conventional wisdom. The book explores how incentives play a crucial role in various aspects of life, from crime to elections, and emphasizes the importance of looking at data objectively to understand the reality of situations. It also highlights that the conventional wisdom is often incorrect, and encourages readers to think critically and ask questions about commonly accepted beliefs.