Empirical work in the social studies of science has progressed rapidly with the availability and development of the citation indexes. Citation counts have become a widely accepted measure of the quality of a scientific contribution. However, there are several problems involved in the use of citation counts as a measure of quality in science. First, citation counts are sensitive to popular trends in science. In this sense, they approximate a Nielsen rating for science. Second, the distribution of citations restricts their utility to separating the extremes. Third, citation counts are not sensitive to the ethical and moral dimensions of the quality of a scientific contribution. Fourth, citation counts underestimate the contribution of applied scientists. This paper examines these limitations.