I have the same problem with my computer. Unfortunately you'll just have to ignore it. Evidently your graphics card does need updating, of perhaps its something else. Although this isnt a problem if your going to distribute the game, just because the graphics arent too good on your computer doesnt mean it will be the same on another.
i also had an old computer but didnt get any problem with the terrain texture. Just guessing, it might be something with the draw distance. Of course, it may also be because of the absence of a better graphics solution.