Keep in mind that white paint is a lot harder than many colors so while it may work great on white it could seriously mar black paint.
I don't doubt that the Mr. Clean pads do a good job but I would recommend going with a detail clay for an overall cleaning. Clay bar your car a single time and it will make you a believer. The advantage of the clay bar is that after removing the contaminate from the car it is removed from the working surface so you are not scratching the "lifted junk" against your paint surface.
Great tutorial on using clay here -
Autopia - Detailing Clay & Pre-wax Cleaning
I have used both Clay Magic (cheapest and my favorite) and Meguires Clay bars with great success.
Try placing your finger inside a ziploc bag and running it along the paint before and after using the clay bar. There will be a huge difference in smoothness.