At high area fractions, monolayers of colloidal dimer particles form a degenerate crystal (DC) structure in which the particle lobes occupy triangular lattice sites while the particles are oriented randomly along any of the three lattice directions. We report that dislocation glide in DCs is blocked by certain particle orientations. The mean number of lattice constants between such obstacles is Z̄exp=4.6±0.2 in experimentally observed DC grains and Z̄sim=6.18±0.01 in simulated monocrystalline DCs. Dislocation propagation beyond these obstacles is observed to proceed through dislocation reactions. We estimate that the energetic cost of dislocation pair separation via such reactions in an otherwise defect free DC grows linearly with final separation, hinting that the material properties of DCs may be dramatically different from those of 2-D crystals of spheres. © 2008 The American Physical Society.