A full quantum calculation of several transport properties for the helium-nitrogen molecular mixture has been carried out within the coupled state (CS) approximation using the HFD1 potential energy surface (PES) that has already been employed as a test potential in various other calculations. Comparison of the ensuing observables, both for values at given total energies and for values as function of temperature, with the essentially exact close coupling (CC) results and with infinite-order-sudden (IOS) approximate calculations (all obtained with the same HFD1 potential function) indicate an average percentage error for diffusion and viscosity ranging between 1% and 3% with respect to the CC results, while the viscomagnetic relaxation data exhibit a much more marked difference between CC and CS calculations. The physical origins of such differences, as well as explanations for those situations where close agreement is found between different dynamical approximations, are discussed in detail. Possible predi...