Biological processes such as DNA replication, RNA transcription, and protein translation operate with remarkable speed and accuracy in selecting the right substrate from pools of chemically identical molecules. This result is obtained by non-equilibrium reactions that dissipate chemical energy. It is widely recognized that there must be a trade-off between speed, error, and dissipation characterizing these systems. In this paper, we quantify this trade-off using tools from mathematical optimization theory. We characterize the Pareto optimal front for a generalized version of Hopfield's kinetic proofreading model, which is a paradigmatic example of biological error correction. We find that models with more proofreading steps are characterized by better trade-offs. Furthermore, we numerically study scaling relations between speed, accuracy, and dissipation on the Pareto front.