Most known pathogenic mutations occur in protein-coding regions of DNA and change the way proteins are made. Taking protein structure into account has therefore provided great insight into the molecular mechanisms underlying human genetic disease. While there has been much focus on how mutations can disrupt protein structure and thus cause a loss of function (LOF), alternative mechanisms, specifically dominant-negative (DN) and gain-of-function (GOF) effects, are less understood. Here, we investigate the protein-level effects of pathogenic missense mutations associated with different molecular mechanisms. We observe striking differences between recessive vs dominant, and LOF vs non-LOF mutations, with dominant, non-LOF disease mutations having much milder effects on protein structure, and DN mutations being highly enriched at protein interfaces. We also find that nearly all computational variant effect predictors, even those based solely on sequence conservation, underperform on non-LOF mutations. However, we do show that non-LOF mutations could potentially be identified by their tendency to cluster in three-dimensional space. Overall, our work suggests that many pathogenic mutations that act via DN and GOF mechanisms are likely being missed by current variant prioritisation strategies, but that there is considerable scope to improve computational predictions through consideration of molecular disease mechanisms.