The evolution of a perturbation from a local source upon the Mandelstam-Brillouin scattering in a plasma layer of a finite thickness and infinite length is examined analytically. It is shown that, in the course of time, the perturbation can either leave the scattering region through one of the two layer boundaries or propagate along the layer with a velocity that is lower than the velocity of propagation of the sound wave and with the amplitude that either exponentially increases or decreases. In the particular case of strictly backward scattering (the scattering angle is π), this propagation velocity is zero. The instability threshold fields and instability increments are calculated taking into account both convective losses and collisional damping of waves. It is shown that the instability threshold for scattering at an arbitrary angle can be lower than that for strictly backward scattering, and, if the intensity threshold of the pump wave is exceeded little, the scattering increment at an angle can also be higher than the increment for backward scattering. If the threshold is exceeded greatly, so that convective losses can be neglected, the greatest increment is observed for backward scattering.