I added this as a subtask of RT-2299 since it is related to multi-monitor support, which is not supported in the 1.0 release.

If you create a group with cache: true then any child nodes will not render once dragged across screens in a multi-monitor environment. This is easily reproducible with the following code:
Stage {
    scene: Scene {
        width: 200
        height: 200
        content: Group {
            cache: true
            content: Rectangle {
                width: 200
                height: 200
                fill: Color.BLUE
            }
        }
    }
}

When dragged across screens, the blue rectangle will turn black.

I have a rather elaborate hack for now that works as a drop-in replacement for Group and flips cache to false, and then back to true when a Node is dragged across screens. See org.jfxtras.scene.CacheSafeGroup in the JFXtras project for more details:
http://code.google.com/p/jfxtras/