The display glitch you are seeing on your model is a common 3D graphics artifact called Z-fighting.
Z-fighting is a phenomenon in 3D rendering that occurs when two or more primitives have similar values in the z-buffer. It is particularly prevalent with coplanar polygons, where two faces occupy essentially the same space, with neither in front. Affected pixels are rendered with fragments from one polygon or the other arbitrarily, in a manner determined by the precision of the z-buffer.
Basically what is happening is when two coplanar faces occupy the exact same space Blender doesn't know which of the two faces to render. The faces are "fighting" which one is closer to the camera. So due to floating-point calculations in the distance to the camera (z-buffer), various points of the shared surface are rendered as one of the faces, and other parts are rendered as the other face. This results in the strange looking Moire-like glitch you are witnessing.
To fix this problem you can first try to remove double vertices with W > Remove Doubles. This will merge vertices which occupy essentially the same location, you can adjust the tolerance in the F6 parameters menu immediately after removing doubles. In some cases removing doubles won't be enough to fix the z-fighting, in these cases you will just have to go through manually and remove the overlapping faces.
I suggest you read up on manifold and non-manifold geometry.