Disorder is shown to induce qualitative changes in the electronic spectrum and hence in the response of assemblies of quantum dots. Lattices of quantum dots have one unique source of disorder: the dots themselves can be prepared with a narrow distribution of properties but they are never quite identical. This is unlike a lattice of atoms or molecules. In addition, lattices of quantum dots have a configurational disorder and can also be prepared with compositional disorder. The relaxation of selection rules and the splittings of degeneracies due to symmetry breaking induced by these fluctuations can be probed by optical means. Special attention is given to the enhancement and to the variation of the second harmonic response as a function of the spacing between the dots.