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When mirroring meshes, vertex groups aren't mirrored for center vertices
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When creating bone weights for a mirrored mesh, all vertices that are on the mirror plane are influenced only by the bones of the original side (i.e. if you model the +x side of a mesh and mirror both it and the armature to fill the -x side, the points on the mirror plane are affected exclusively by the +x side).

In the attached .blend file, in 2.62, rotate the left and right bones around the Y axis. Notice that the four vertices in the center are affected only by one side, while they should be affected by both sides: this breaks symmetry when the movement of bones is mirrored. Explicitly setting the center vertices to have the weights of both bones would eliminate this behavior, but this is infeasible with complex models with more organic weight painting.

--Environment Specifications--
Windows 7 Home Premium, 64 bit
AMD Radeon 6770
Intel Core i7 2600