  We carried out Raman measurements on neutron-irradiated and Al-doped MgB$_2$
samples. The irradiation-induced topological disorder causes an unexpected
appearance of high frequency spectral structures, similar to those observed in
lightly Al-doped samples. Our results show that disorder-induced violations of
the selection rules are responsible for the modification of the Raman spectrum
in both irradiated and Al-doped samples. Theoretical calculations of the phonon
density of states support this hypothesis, and demonstrate that the high
frequency structures arise mostly from contributions at ${\bf q}\not=0$ of the
E$_{2g}$ phonon mode.
