High publication demands and the low acceptance rate of peer review journals place the journal editors and their reviewers in a powerful position. Journal reviewers have a vital role not only in influencing the journal editor's publication decisions, but also in the very nature and direction of scientific research. Because of their influence in peer review outcomes, journal reviewers are aptly described as the "gatekeepers of science." In this article we describe several pitfalls that can impede reviewers' impartial judgement. These include such issues as confirmatory bias, the negative results bias (the file drawer problem), the Matthew effect, the Doctor Fox effect, and gender, race, theoretical orientation, and "political correctness." We argue that procedures currently used by many professional journals, such as blind or masked review, may not completely alleviate the effects of these pitfalls. Instead, we suggest that increasing reviewers' awareness of the pitfalls, accountability, and vigilance can improve fairness in the peer review process. The ultimate responsibilities belong to the journal editors who are confronted with the difficult task of satisfying journal readers, contributors, reviewers, and owners. We recommend that the journal editors conduct periodic internal and external evaluations of their journals' peer review process and outcomes, with participation of reviewers, contributors, readers and owners.