We discuss the use of convolutional codes to perform concurrent error detection (CED) in finite state machines (FSMs). We examine a previously proposed methodology, we identify its limitations, and we outline two improvements that reduce its cost and enhance its effectiveness. More specifically, we demonstrate how the existing FSM hardware can be reused for computing the convolutional code keys and we formulate the optimization problem of maximizing hardware reusability. Additionally, we extend the proposed methodology to detect errors that only affect the output logic but not the next state of the FSM, which are not detected by the previously proposed methodology.