As I got some remarks from people about the blurry backgrounds, I worked on fixing this issue.
The original backgrounds have been captured in a resolution of 1920×320. But the iPhone can have a maximum texture size of 1024×1024. The solution was to cut the backgrounds in 4 480×320 images. And now we show the backgrounds using a orthographic projection to avoid seeing seams between OpenGL ES rendered triangles.
Here you see some examples of before and after results: