I have an array of planes that I textured with an image file I made. When I look at the array in Texture mode or Render mode, I can see white lines bleeding through between the planes:
I don't know how well the problem shows in these images.
I have done some research and found out that it is sometimes caused by bleeding of the alpha channel when the UV mapping is on the edge of an image where the transparency color in the image file is white instead of black. I tried fixing my image files in Krita (where I made them) and I think I turned off the alpha or at least changed it from white to black, which reduced the problem somewhat, but not completely. (I'm just learning how to use Krita)
I also moved the edges of the UV mapping away from the edges of the image file, which helped a little more. But again, not completely.
I also read that this can be caused by MIP-mapping, which I know very little about. I tried changing a few settings in the Materials and Textures windows, and one of them helped reduce the bleeding in render mode, but they're still quite visible at certain angles or (more significantly) when moving the camera.