The core idea of evolutionary medicine is simple enough. Analyze traits that leave organisms vulnerable to disease to try to understand why natural selection did not do better. But to actually do this turns out to be very difficult. Few of the problems are technical, most are conceptual. It is very hard for people to recognize that diseases themselves do not have evolutionary explanations, and harder yet for them to systematically list all possible explanations and the evidence for and against each one. After years of trying to help students get this all straight, I wrote the "Ten Questions" paper to be as close to a Betty Crocker recipe for aspiring evolutionary medicine researchers as I could. Some have told me it helps. For a different, more negative version that lists common errors, see the Table in my chapter in the Trevathan volume.
The most common and serious mistake in evolutionary medicine is viewing diseases as adaptations. Diseases are not traits shaped by natural selection; they do not have direct evolutionary explanations. However, the insight at the core of evolutionary medicine is that most traits universal in a species that make bodies vulnerable to disease were shaped by natural selection; they need evolutionary explanations, often a combination of several.