  We study the effects of disorder in the electronic properties of graphene
multilayers, with special focus on the bilayer and the infinite stack. At low
energies and long wavelengths, the electronic self-energies and density of
states exhibit behavior with divergences near half-filling. As a consequence,
the spectral functions and conductivities do not follow Landau's Fermi liquid
theory. In particular, we show that the quasiparticle decay rate has a minimum
as a function of energy, there is a universal minimum value for the in-plane
conductivity of order e^2/h per plane and, unexpectedly, the c-axis
conductivity is enhanced by disorder at low doping, leading to an enormous
conductivity anisotropy at low temperatures.
