Molecular-continuum methods, as considered in this work, decompose the computational domain into continuum and molecular dynamics (MD) sub-domains. Compared to plain MD simulations, they greatly reduce computational effort. However, the quality of a fully two-way coupled simulation result strongly depends on a variety of system-specific parameters, and the corresponding sensitivity is only rarely addressed in the literature. Using a state-flux molecular-continuum coupling algorithm, we investigated the influences of various parameters, such as the size of the overlapping region, the coupling time step and the quality of ensemble-based sampling of flow velocities, in a Couette flow scenario. In particular, we considered a big setup in terms of domain size and number of time steps, which allowed us to investigate the long-term behavior of the coupling algorithm close to the incompressible regime. While mostly good agreement was reached on short time scales, it was the long-term behavior which differed even with slightly differently parametrized simulations. We demonstrated our findings by measuring the error in velocity, and we summarize our main observations with a few lessons learned.