In this note, we consider a broad class of dynamic scheduling problems associated with a single-server, multiclass, continuous-flow manufacturing system. Using a general framework, we provide conditions under which the solution to these problems is the implementation of a class of production controls called myopic scheduling policies. The proof of optimality, which is intuitively appealing, applies to more general production models than existing proofs in the literature, which typically either use the maximum principle or solve the Hamilton-Jacobi-Bellman (HJB) equation. We also present several counterexamples that explicitly illustrate the potential limitations of myopic scheduling policies.