display bug

Different behaviors take control of different layers. But generally a layer can only be controlled by one behavior. So what can happen is if the same layer ends up with two things trying to control it, things can go weird. Tagging (and handles) is very important here as tags is how behaviors find the layers to take control of. (The layer names are used to automatically create tags to save you effort, but as you edit a puppet you can end up with stray or extra tags - causing this sort of problem.)

The tags are over in the properties. I would spend a little time and go through every layer of the puppet in rig mode and check the tags on each layer (does not take that long). Are there extra unexpected tags there? I prefer the "A" icon to show tag names rather than the graphical representation - easier to see which tags are on (personal preference).

Another approach is to turn on the mesh icon at the bottom of the scene panel. It will put lots of yellow triangles all over the artwork while you move your head around. You will probably see one point is "stuck", not moving. That can help pinpoint which part of the puppet has gone wrong. I would check those tags first. Also if left side of face is okay but right side is not, then compare the two layer trees. If you just cloned the artwork, you might have a "Right" layer and tag on the left side, which makes things go wacky.

This problem is pretty common and definitely fixable. Finicky, but once you get the tags right things will start working.

Oh, and if not tags, independence of layers is the next thing to look at. And handles. E.g. putting a tag on a layer and on a handle in that layer is not the same thing, and can also contribute to these sorts of problems. But I would start checking tags first.