  Spin excitation spectrum is studied in the double exchange model in the
presence of disorder. Spin wave approximation is applied in the lowest order of
1/S expansion. The disorder causes anomalies in the spin excitation spectrum
such as broadening, branching, anticrossing with gap opening. The origin of the
anomalies is the Friedel oscillation, in which the perfectly polarized
electrons form the charge density wave to screen the disorder effect. Near the
zone center $q = 0$, the linewidth has a $q$ linear component while the
excitation energy scales to $q^2$, which indicates that the magnon excitation
is incoherent. As $q$ increases, there appears a crossover from this incoherent
behavior to the marginally coherent one in which both the linewidth and the
excitation energy are proportional to $q^2$. The results are compared with
experimental results in colossal magnetoresistance manganese oxides.
Quantitative comparison of the linewidth suggests that spatially-correlated or
mesoscopic-scale disorder is more relevant in real compounds than local or
atomic-scale disorder. Comparison with other theoretical proposals is also
discussed. Experimental tests are proposed for the relevance of disorder.
