superimposed mesh wobbles and flickers during animation cycle

I added to the main character a flat cartoon mouth (let's call M1 for sake of simplicity), childed to the head joint and superimposed to the mouth of the mesh: when playing the animation (a simple walk), M1 wobbles and the color of the underneath polygons flickers for some seconds. I tried with moving M1 some millimeters in z, but this doesn't solve the issue. Why all this?