Mesoscale objects with unusual structural features may serve as the analogues of atoms in the design of larger-scale materials with novel optical, electronic or mechanical behaviour. In this paper we investigate the structural features and the equilibrium dynamics of micrometre-scale spherical crystals formed by polystyrene particles adsorbed on the surface of a spherical water droplet. The ground state of sufficiently large crystals possesses finite-length grain boundaries (scars). We determine the elastic response of the crystal by measuring single-particle diffusion, and quantify the fluctuations of individual dislocations about their equilibrium positions within a scar by determining the dislocation spring constants. We observe rapid dislocation glide with fluctuations over the barriers separating one local Peierls minimum from the next and rather weak binding of dislocations to their associated scars. The long-distance (renormalized) dislocation diffusion glide constant is extracted directly from the experimental data and is found to be moderately faster than single-particle diffusion. We are also able to determine the parameters of the Peierls potential induced by the underlying crystalline lattice.