A basic object in TGD will have at least a multi-shader and a default shader i.e. at least one surface. Whether it's an image map or just a colour is irrelevant, it still has a surface, and displacement is a property of that surface.
Here is a screengrab from a tree object of the default shader for the bark. In this case the displacment is set to 0.01 (1cm). Some objects I've imported that displayed the same "sticks" as your render had a displacement of 1. Setting these to 0 fixed the problem.
Hope this helps.
The white dots I suspect are a result of the render quality setting in the population. (second screen grab)