We determine the ultimate quantum limits on the estimation of a "mode parameter" that modifies the spatiotemporal structure of the modes occupied by a parameter-independent quantum state. Our analytical expression for the quantum Cramér-Rao bound for arbitrary multimode states, pure or mixed, Gaussian or non-Gaussian, reveals the origin of quantum precision enhancements that may be achieved with nonclassical states. Improved scaling of the estimation error is possible only if specific modes are populated and measured. Our results allow us to identify quantum-enhanced estimation strategies for a wide range of spatio-temporal mode parameters and in superresolution imaging.