Without proper care and maintenance, any new car's paint can quickly come to resemble decades-old sandpaper. The trick to keeping your car looking like new is to remember that dirt and dust are abrasives, especially when ground into the paint by careless washing. The good news is that most new cars are made with harder and smoother paint compounds than older models, which makes washing and maintaining them simpler and easier than ever.
To keep your car's paint shiny and smooth, you must avoid grinding surface contaminants into the clear coat. Old style brushes (no matter how soft) have a nasty habit of collecting dirt particles and pressing them into the paint, which is why any professional detailer will use a slip-on wash mitt made of soft and lint-free material. When used with a light tough, wash mitts do a fine job of containing contaminants without pushing them into the surface. Aside from any material considerations, a wash mitt will never flip over and accidentally ding the paint job.
Soaps and detergents are not the same thing. Soaps usually use animal byproducts (like glycerine) and natural materials (like lye) to act as a surfactant. Surfactants (used in both soaps and detergents) lift dirt and contaminants from the substrate, but the materials used in soaps often react with the minerals in your water to form a surface film. You should always use a dedicated detergent designed for cars; dish and laundry detergents (which are essentially degreasing solvents) will strip your car's paint of crucial molecules designed to keep it soft and pliable enough to resist damage. Although washing the car with non-car detergents probably won't hurt anything the first time, consistent use will make the paint brittle and more prone to damage from abrasives like dirt and dust. Car detergents are not only milder than other types, but most contain conditioners to help replace what the cleaning surfactants strip away. Think of it like a combination shampoo/conditioner for your car. Incidentally, this is exactly what most commercial car washes are; you could actually use household shampoo/conditioner to wash the car, but this can get expensive in no time.
All detergents have some sort of softening agent that prevents water-soluble minerals like iron and calcium from sticking to the surface, but none are perfect. The best way to keep minerals from sticking to your paint (and later embedding in it) is to wash the car with "soft" (mineral-free) water. While doing so might seem a little high maintenance, the fact is that no professional detailer would consider washing a high-end car with hard tap water. No softener will completely eliminate all minerals and chlorine (bleach) in the water, but the detergent-borne softeners should take care of the rest. In-line water softeners and deionizers (which screw into line between the water source and hose) will remove most of the water-borne minerals, which should almost eliminate the need for hand drying to prevent water spots.