We present a systematic study of interface roughness and its effect on coherent dynamical processes in quantum dots. The potential due to a sharp, flat interface lifts the degeneracy of the lowest energy valleys and yields a set of valley eigenstates. Interface roughness is characterized by fluctuations in the location of the interface and in the magnitude of the potential step. Variations in the position of the interface, which are expected to occur on the length scale of the lattice constant, reduce the magnitude of the valley-orbit coupling. Variations in the size of the interface potential step alter the magnitude of the valley-orbit coupling and induce transitions between different valley eigenstates in dynamics involving two (or more) dots. Such transitions can be studied experimentally by manipulating the bias between two dots and can be detected by charge sensing. However, if the random variable characterizing the position of the interface is correlated over distances on the order of a quantum dot, which is unlikely but possible, the phase of the valley-orbit coupling may be different in adjacent dots. In this case tunneling between like and opposite valley eigenstates is in effect a random variable and cannot be controlled. We suggest a resonant tunneling experiment that can identify the matrix elements for tunneling between like and opposite valley eigenstates.