We present a calculation of the neutrino-nucleon scattering cross-section which takes into account the nuclear correlations in the relativistic random phase approximation (RPA). Our approach is based on a quantum-hadrodynamics model with exchange of sigma, omega, pi, rho and delta mesons. In view of applications to neutrino transport in the final stages of supornova explosion and proto-neutron star cooling, we study the evolution of the neutrino mean free path as a function of density, proton-noutron asymmetry and temperature. Special attention was paid to the issues of renormalization of the Dirac sea, residual interactions in the tensor channel, coupling to the delta-meson and meson mixing. In contrast with the results of other authors, we find that the neutral-current process is not sensitive to the strength g(l) of the residual contact interaction. As a consequence, it is found that RPA corrections with respect to the mean-field approximation amount to only 10% to 15% at high density.