I'm making a short animated video in blender, and I have a model of a TV with an image texture on the screen. When the TV moves, the image texture does not move very smoothly, and wiggles.
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
Or you can try to model screen like here.