We study the stability and evolution of various elastic defects in a flat graphene sheet and the electronic properties of the most stable configurations. Two types of dislocations are found to be stable: 'glide' dislocations consisting of heptagon&-pentagon pairs, and 'shuffle' dislocations, an octagon with a dangling bond. Unlike the most studied case of carbon nanotubes, Stone Wales defects seem to be dynamically unstable in the planar graphene sheet. Similar defects in which one of the pentagon&-heptagon pairs is displaced vertically with respect to the other one are found to be dynamically stable. Shuffle dislocations will give rise to local magnetic moments that can provide an alternative route to magnetism in graphene.