We present a comparative study of structural and magnetic properties of the as-grown and annealed samples of double perovskite, La2CoMnO6. The single monoclinic (P21/n) phase has been achieved for both the samples. Electron microscopy highlights the change in morphology of the as-grown and annealed samples, with the annealed sample having more grain boundaries and bigger particle sizes. The annealing in presence of oxygen leads to increase in the population of antiphase boundaries, which is supported by the decreases in the remanent and saturation magnetizations. An analysis of magnetization dynamics by means of AC susceptibility shows four different magnetic transitions, with two high temperature ferromagnetic transitions and two cluster glass-like states emerging at low temperatures, which appear almost identical in both the as-grown and annealed samples.