The lattice and rotational dynamics of K1-x(ND4)xI mixed crystals have been investigated by means of coherent inelastic neutron scattering as a function of the ammonium concentration and temperature. As the temperature is lowered, anomalies in the behaviour of transverse acoustic phonons propagating along the fourfold axis have been found. These are, firstly, a relaxational behaviour in the phonon energy and acoustic damping for x=0.42 and x=0.62 and, secondly, the existence of a dynamical central peak in the mixed and pure systems. For the three compounds investigated, the neutron data are interpreted in terms of coupling between dipolar orientational fluctuations and transverse acoustic phonons propagating along the fourfold axis. This rotation-translation coupling is efficient for wavevectors q*>or=0.5, but its strength is largest at the Brillouin zone boundary (the X point). Finally the overall dynamical response measured by neutron scattering suggests a collective slowing down of the ND4+ dynamics on lowering the temperature.