Some of that looks more the angle of the sun, either overhead, or just in front of you. It's striking the front of the lens and sometimes washing out the image, sometimes just highlighting the odd mark on the lens. (Unfortunately, getting everything from bugs to oil spots and dust etc on the lens is inevitable especially where it can be thrown up off your own wheels.
the frame rate, (sort of the equivalent for shutter speed on a still camera), will make a big difference to picture quality on a moving vehicle like a Westfield. Generally speaking, you want as high as possible. 60 fps (frames per second) works really well. It will also, normally, dramatically reduce any rolling shutter artefacts - that odd shimmering jelly wobble like quality you can see in the first clip. It's essential caused by the vibration from the car interfering with the way the sensor in the camera records the image.