The integral three-dimensional (3D) display is an ideal visual 3D user interface. It is a display method that fulfills many of the physiological factors of human vision. However, in integral 3D displays for mobile applications that use direct-view flat panels to display elemental images, color moiré is a problem that occurs because of the sampling of subpixels by elemental lenses and the insufficient resolution and depth reproduction of the reconstructed 3D image. In the conventional moiré reduction method, the degree of defocus of elemental lenses has to be set to a large value, which is one of the factors that reduces the performance in terms of depth reproduction. In contrast, only one-step optics can be installed and the installation positions are limited in the conventional wobbling method. This is because, in the method, which uses a birefringent optical element, two-step optics are thicker than the focal length of the lens array. For this reason, it was difficult to achieve ideal moiré reduction and depth reproduction performance improvements. To solve these problems, we propose a method that utilizes multiple optical wobbling spatiotemporal multiplexing using polarization diffractive elements and liquid-crystal polarization controllers. Using the proposed method, the wobbling optics can be designed to be thin, allowing two-step optics to be installed between the display panel and lens array. When the moiré modulation degree without wobbling is normalized as 100%, it decreases to 25% with wobbling. The proposed method not only achieves effective color moiré reduction without deteriorating the 3D image quality, but also can double the resolution of the elemental images to improve the depth reproduction.