You seem to have two identical shapes and polygons in exactly the same places. One set of polygons has the texture and the other doesn't. Double-check this by right-click selecting anything in that space. Then press M and 2 moving whatever was selected to Layer 2. Whatever geometry stays behind will tell you which object, textured or not, you selected.
X Delete what's not needed. If what you needed was moved to the second Layer, press 2 along the number row (not numpad) and Right-Click select it and press M and 1 to move it to the first layer.
Blender Render and Cycles do not play well with sheets of polygons in identical locations.