If by "we" you mean "scientists," then it is extremely important that we gain as detailed an understanding of evolutionary mechanisms and the patterns of diversification that they have produced as we can. The question of the origins of biological diversity is a fundamental one, and obtaining as complete an answer as possible is a primary goal of the life sciences. Evolution is to biology what the periodic table is to chemistry: It makes sense of otherwise disconnected pieces of information and provides the framework for further investigation.
If you mean "students enrolled in science programs," either undergraduates or grad students (as in our study), then I would say that a good working knowledge of evolutionary theory, though not a full understanding of all its nuances, should be a major goal. Again, evolution is the unifying principle of biology, and without grasping how it works, one cannot make sense of the history and current diversity of life on this planet. Most science majors will not go on to become professional evolutionary researchers, but many will become teachers, researchers in industry or government, consultants, doctors, politicians, or any of a wide range of careers in which a working knowledge of evolution is important. As I tell the students in my course when I discuss why they should work hard to understand evolution, if the goal is to have a scientifically literate public, who but the future teachers and other educated citizens can make that happen?
If you mean "members of the public at large," then I would say that at least a basic understanding of evolution is still important, if not for academic reasons then for pragmatic ones. Evolutionary knowledge informs decisions in medicine, agriculture, resource management, and many other areas. If, as I am sure most biologists feel, an understanding of evolution is important at all levels, then it is important that it be taught -- and taught properly -- from elementary school to graduate school. A population that recognizes the standing and relevance of evolutionary principles is one that will support this endeavor, whereas one that misunderstands or fears evolutionary biology will seek to undermine science education. There is an inevitable feedback loop in this regard, and effective education is the way to make it a positive one.
How detailed an understanding of evolution do we need? It depends on who "we" are -- but "very little" is not the answer in any case.
How detailed an understanding of evolution do we need?
The folks over at Science and Religion Today were interested in our study on graduate student conceptions of evolution, and asked me to give some thoughts on the question "How detailed an understanding of evolution do we need?" Here is my answer.