I am not really sure, but since no one else has answered here are a few thoughts:
1. It seems like maybe the texture is somehow stuck in World space as you scale the model. Does the same thing happen when you move the model?
2. What kind of mapping are you using? Is the mesh UVW unwrapped or are you using the UVW Map set to box or something? Is any part of your texture procedural?
3. Are any of the material parameters animated?
4. What does your modifier stack look like?
4. Only 1 surface (the surface facing the camera) of the model seems to be affected. Do you have a multi-material assigned? The inner orange colored portion of the mesh doesn't seem to be moving differently than the mesh, but it is difficult to tell because it is mostly a solid color. It looks mostly like the cellular noise type material is misbehaving.
The more details you provide about the specific mesh and material parameters you have, the better the chance that someone will be able to help. Hope this shakes something loose for you.
