Yes, rigging screenshot would be a big help. Another useful trick is in the scene panel turn on the mesh icon at the bottom of the panel. It draws yellow triangles over the mesh. Then move the character around and it becomes clearer which part of the mesh is not moving. There is probably something there tagged incorrectly. I am guessing something near the eyes.
Layers generally cannot be controlled by two things, so if a layer gets extra tags, the normal "owner" can be changed, so instead of the Face behavior (for example) moving that part of the face, something else jumps in and grabs control, meaning the Face behavior cannot move it anymore. Its fixable, just need to understand the rigging hierarchy of the puppet (the nesting of layers) to spot it. (Also handles, but they can be harder to see from screenshots unfortunately.)