  We have studied the interlayer resistivity of the prototypical
quasi-two-dimensional organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$
as a function of temperature, current and magnetic field, within the
superconducting state. We find a region of non-zero resistivity whose
properties are strongly dependent on magnetic field and current density. There
is a crossover to non-Ohmic conduction below a temperature that coincides with
the 2D vortex solid -- vortex liquid transition. We interpret the behaviour in
terms of a model of current- and thermally-driven phase slips caused by the
diffusive motion of the pancake vortices which are weakly-coupled in adjacent
layers, giving rise to a finite interlayer resistance.
