We have studied the ordering dynamics of a two-dimensional system which consists of a single layer of spherical block copolymer microdomains in a thin film. We follow the annealing process after a quench from the disordered state by electron microscopy and time-lapse atomic force microscopy. At late times the orientational correlation length ξ6 of the microdomain lattice exhibits a t1/4 temporal power law. We compare the time evolution of the densities of dislocations, disclinations and the dislocation orientational correlation function. While most disclinations condense into dislocations and most dislocations condense into "grain boundaries", the dynamics appear to involve the interplay of disclinations and lines of dislocations. Rather than isolated grains shrinking, the most frequently observed process is the collapse of a smaller grain which resides on the boundary of two larger grains.