  We study the two-particle spectral functions and collective modes of weakly
disordered superconductors using a disordered attractive Hubbard model on
square lattice. We show that the disorder induced scattering between collective
modes leads to a finite subgap spectral weight in the long wavelength limit. In
general, the spectral weight is distributed between the phase and the Higgs
channels, but as we move towards half-filling the Higgs contribution dominates.
The inclusion of the density fluctuations lowers the frequency at which this
mode occurs, and results in the phase channel gaining a larger contribution to
this subgap mode. Near half-filling, the proximity of the system to the charge
density wave (CDW) instability leads to strong fluctuations of the effective
disorder at the commensurate wave-vector ($[\pi,\pi]$). We develop an
analytical mode coupling approach where the pure Goldstone mode in the long
wavelength limit couples to the collective mode at $[\pi,\pi]$. This provides
insight into the location and distribution of the two-particle spectral weights
between the Higgs and the phase channels.
