Image textures 'wiggling' when the mesh moves?

ISSUE

Problem is TV screen topology (not Material or assigned Armature). Screen is ngon that doesnt have enough geometry in surface. You have curved edges, but there is not an information how to model surface. So blender generates some :)

In viewport it looks flat ...

... but for rendering are ngons triangulated. What Happens with surface when rendered you can see when in edit mode search for Triangulate Faces

QUICK FIX

Simplify corners, delete screen face, select border with active vertex (white) in corner

and search for Grid Fill, set Span to 16 in my case.

To make screen edge sharp after Shade Smooth, select it and search for Mark Sharp

Easy check surface with some Matcap view type

Or you can try to model screen like here.