The aim of the present work is to study MHD waves and instabilities at contact discontinuities, in a plasma, with applications to the solar atmosphere. In particular we investigate what effect field inclination has on the characteristics of waves and instabilities. We initially consider the gravity-free environment and investigate the characteristics of magneto-acoustic surface waves propagating at a single density interface, in the presence of an inclined magnetic field. For linear wave propagation, dispersion relations are obtained for both the time independent and the incompressible, time-dependent cases. Analytical solutions are derived for small inclination angle. For the time-independent case, the inclination of the field renders the frequency of waves to be complex, where the imaginary part describes wave attenuation, due to lateral energy leakage. The time-dependent case confirms the attenuation of leaky waves at a contact discontinuity. We also discuss the transition to the tangential discontinuity as the inclination angle tends to zero. We show that there is no continuous transition from the leaky modes on a contact discontinuity to the surface modes on a tangential discontinuity. However, such a transition exists if we take the average quantities describing the leaky modes. We extend our study of the effects of magnetic field inclination at a contact discontinuity, by including the gravitational effects. We investigate the nature of the magnetic Rayleigh-Taylor instability at a density interface permeated by an inclined magnetic field in the ncompressible MHD limit. Through an ideal MHD analysis, we find that, unlike the tangential case of MRT instability, perturbations of the interface are shown to be unstable for all wavenumbers, thus, due to the inclination of the magnetic field, the critical wavenumber at which waves become unstable disappears. As a result, field inclination produces qualitatively different dynamics than the tangential case, for the gravitationally modified case, as well as for the gravity free analysis. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. Our analysis shows that the observed growth time of instability requires only small values of the inclination angle.