Biological processes that are able to discriminate between different molecules consume energy and dissipate heat, using a mechanism known as proofreading. In this work, we thoroughly analyse the thermodynamic properties of one of the most important proofreading mechanisms, namely Hopfield’s energy-relay proofreading. We discover several trade-off relations and scaling laws between several kinetic and thermodynamic observables. These trade-off relations are obtained both analytically and numerically through Pareto optimal fronts. We show that the scheme is able to operate in three distinct regimes: an energy-relay regime, a mixed relay-Michaelis–Menten (MM) regime and a Michaelis–Menten regime, depending on the kinetic and energetic parameters that tune transitions between states. The mixed regime features a dynamical phase transition in the error-entropy production Pareto trade-off, while the pure energy-relay regime contains a region where this type of proofreading energetically outperforms standard kinetic proofreading.