  The role of Coulomb disorder, either of extrinsic origin or introduced by
dopant ions in undoped and lightly-doped cuprates, is studied. We demonstrate
that charged surface defects in an insulator lead to a Gaussian broadening of
the Angle-Resolved Photoemisson Spectroscopy (ARPES) lines. The effect is due
to the long-range nature of the Coulomb interaction. A tiny surface
concentration of defects about a fraction of one per cent is sufficient to
explain the line broadening observed in Sr$_2$CuO$_2$Cl$_2$, La$_2$CuO$_{4}$,
and Ca$_{2}$CuO$_{2}$Cl$_{2}$. Due to the Coulomb screening, the ARPES spectra
evolve dramatically with doping, changing their shape from a broad Gaussian
form to narrow Lorentzian ones. To understand the screening mechanism and the
lineshape evolution in detail, we perform Hartree-Fock simulations with random
positions of surface defects and dopant ions. To check validity of the model we
calculate the Nuclear Quadrupole Resonance (NQR) lineshapes as a function of
doping and reproduce the experimentally observed NQR spectra. Our study also
indicates opening of a substantial Coulomb gap at the chemical potential. For a
surface CuO$_2$ layer the value of the gap is of the order of 10 meV while in
the bulk it is reduced to the value about a few meV.
