  The interplay of disorder and interactions is a subject of perennial
interest. In this work, we have investigated the effect of disorder due to
chemical substitution on the dynamics and transport properties of correlated
Fermi liquids. A low frequency analysis in the concentrated and dilute limits
shows that the dynamical local potentials arising through disorder averaging
generate a linear (in frequency) term in the scattering rate. Such non-Fermi
liquid behaviour (nFL) is investigated in detail for Kondo hole substitution in
heavy fermions within dynamical mean field theory. We find closed form
expressions for the dependence of the static and linear terms in the scattering
rate on substitutional disorder and model parameters. We argue that the low
temperature resistivity will acquire a linear in temperature term, and show
that the Drude peak structure in the optical conductivity will disappear beyond
a certain disorder $p_c$, that marks the crossover from lattice coherent to
single-impurity behaviour. A full numerical solution of the DMFT equations
reveals that the nFL term will show up significantly only in certain regimes,
although it is present for any non-zero disorder concentration in principle. We
highlight the dramatic changes that occur in the quasiparticle scattering rate
in the proximity of $p_c$. Remarkably, we find that the nFL behaviour due to
dynamical effects of impurity scattering has features that are distinct from
those arising through Griffiths singularities or distribution of Kondo scales.
Relevance of our findings to experiments on alloyed correlated systems is
pointed out.
