  We point out a misleading treatment in the literature regarding to
bound-state solutions for the $s$-wave Klein-Gordon equation with exponential
scalar and vector potentials. Following the appropriate procedure for an
arbitrary mixing of scalar and vector couplings, we generalize earlier works
and present the correct solution to bound states and additionally we address
the issue of scattering states. Moreover, we present a new effect related to
the polarization of the charge density in the presence of weak short-range
exponential scalar and vector potentials.
