Is there a way to use Textured Solid without getting a Backface Culling effect? I am trying to have a blender file using Blender 2.69 that allows you to look around and also see textures.

Putting the shading on GLSL and turning on Textured Solid make the textures render great, but then an effect almost identical to Backface Culling occurs. I would like to avoid this as it makes everything look really weird and removes some important parts of the model. 

Is there a way to avoid the backface culling effect while using Textured solid?
While toggling Textured Solid in Solid view, it will always display culling effect, regardless whether Backface Culling is toggled, I'm not sure if this is made on purpose. So, I think the answer is "no". However, you can always switch to the real Texture View mode in order to turn it off.