I writing an app for the iphone and I would like to save an image from it as the default.png for the next invocation. Is this possible? It seems as if the sandbox doesn't allow you to overwrite anything in its local filesystem.
No, you can't. It used to be possible to make Default.png a symbolic link into your Documents folder, then to rewrite the location it pointed to, but functionality was removed in 3.0. You should file a bug with Apple explaining your needs.