Gene set analysis, which translates gene lists into enriched functions, is among the most common bioinformatic methods. Yet few would advocate taking the results at face value. Not only is there no agreement on the algorithms themselves, there is no agreement on how to benchmark them. In this paper, we evaluate the robustness and uniqueness of enrichment results as a means of assessing methods even where correctness is unknown. We show that heavily annotated (‘multifunctional’) genes are likely to appear in genomics study results and drive the generation of biologically non-specific enrichment results as well as highly fragile significances. By providing a means of determining where enrichment analyses report non-specific and non-robust findings, we are able to assess where we can be confident in their use. We find significant progress in recent bias correction methods for enrichment and provide our own software implementation. Our approach can be readily adapted to any pre-existing package.