UV Mapping a simple cube only shows 2 sides textured I can only get two sides of a simple cube to show the UV Map in Blender properly. Here are my steps:


I add a simple cube (ShiftA > cube)
In edit mode, I add seams to unwrap like a cross (see pic below)
A (select all), U > Unwrap
In UV Editor, create new blank image, draw numbers on it with the paint function
in 3D View Editor, change to "Texture view". 


All normals of the faces show correctly to the outside (blue lines in picture). I can flip the normals of the faces and then I can see the numbers, but slightly darker than the first two. Also, I can only do that trick on 3 of the incorrect faces. The last face, whichever one it is, flips the normals but won't show the UV map.

I have also tried different UV map textures and pictures (such as the built-in UV- or Color-grid)

How can I unwrap with seams so that I don't even need to consider flipping already correct normals?
It sounds to me like a problem with your lighting: texture viewport mode can do some strange things with your lighting. Try adding a sun lamp illuminating the other side, or switching to rendered or material view with the texture applied in the material. I apologize if I am not answering your question appropriately (I am only going off of your text because my browser won't show your picture). Hope this helps :)