Soon after Sarah Palin was elected mayor of the foothill town of Wasilla, Alaska, she startled a local music teacher by insisting in casual conversation that men and dinosaurs coexisted on an Earth created 6,000 years ago -- about 65 million years after scientists say most dinosaurs became extinct -- the teacher said.

After conducting a college band and watching Palin deliver a commencement address to a small group of home-schooled students in June 1997,...