Among papers stating a position on anthropogenic global warming (AGW), 97 % endorse AGW. What is happening with the 2 % of papers that reject AGW? We examine a selection of papers rejecting AGW. An analytical tool has been developed to replicate and test the results and methods used in these studies; our replication reveals a number of methodological flaws, and a pattern of common mistakes emerges that is not visible when looking at single isolated cases. Thus, real-life scientific disputes in some cases can be resolved, and we can learn from mistakes. A common denominator seems to be missing contextual information or ignoring information that does not fit the conclusions, be it other relevant work or related geophysical data. In many cases, shortcomings are due to insufficient model evaluation, leading to results that are not universally valid but rather are an artifact of a particular experimental setup. Other typical weaknesses include false dichotomies, inappropriate statistical methods, or basing conclusions on misconceived or incomplete physics. We also argue that science is never settled and that both mainstream and contrarian papers must be subject to sustained scrutiny. The merit of replication is highlighted and we discuss how the quality of the scientific literature may benefit from replication.