Aircraft windshields and windows are made from a hard durable MIL standard acrylic plastic that has a long service life. However, they are still plastic and can be damaged if not cleaned properly. Aircraft windshields and windows are not only expensive, but changing them takes a lot of expensive labor. Paper towels are made from a matrix of processed wood fibers that can be hard enough to scratch plastic. Paper towels will not damage the acrylic every time they are used, but consistently using them will eventually give you little fine scratch defects that refract light differently than an adjacent smooth surface. The small differences in light refraction will obstruct and distort your view.  

Dust is made up of many little abrasive particles so it is important to isolate the dust particles from the windshield as you wipe. The softer and more expanded the cloth material is, the greater the tendency for the cloth to absorb the dust particles isolating them from the cloth surface. In other words, the dust particles can go deeper into a soft fiber matrix as compared to a harsh hard fiber matrix of paper towels. Dust and dirt particles tend to collect on the hard paper towel surface giving it a sandpaper effect. Gently feel a paper towel surface. Gently feel a T-shirt or micro fiber cloth. The surface hardness is very noticeable. 

In summary, there are really two differences in a paper towel and a soft fiber cloth. One difference is the hardness of the actual fiber and the second is the ability of the fiber matrix to absorb dust particles away from the fiber surface. 

Scrubbing the window with your hand is most effective as the cleaner is not being absorbed by a rag. This process gives the cleaner time to soak into the bugs and dirt while distributing the cleaner evenly. A very small rag wet with the cleaner or a VERY SOFT bristle brush also works well. Wash your hands after you are done.

There are two types of cloth that work well to prevent scratching on plastics.

The first is the synthetic micro fiber cloth. This soft supple fine matrix cloth will do an excellent job of protecting the acrylic surfaces. The down side of this cloth is that it is expensive and the wax and polymers used in plastic cleaners do not wash out well. The microfiber cloth will have to be thrown away when the wax and dirt buildup prevents a streak free surface.

The other cloth that works well is soft cotton cloth, with the best construction being T-shirt material. The fluffed soft cotton fibers have layers that isolate dust and dirt well from the cloth surface and they can be used many times. The cost is low enough that you can just throw them away when they get contaminated.

D A M window cleaner is a mixture of non-toxic wax, polymers, and a mild detergent with the slightest trace of alcohol. It is an irritant to the eyes if it has direct contact.  

The polymers and carnauba wax in D A M window cleaner lubricate and encapsulate the abrasive dust and dirt particles so they slide on the plastic surface until they are absorbed deep into the wipe-off towel. The dust and dirt particles are still there, but they cannot get a damaging grip on the plastic surface. After the D A M cleaner is polished off it leaves a protective film that also helps prevent abrasion penetration of dust and dirt particles.

Never wipe a plastic surface when it is dry (or extensively while wet with just water) as some of the abrasive particles will be gouged into the surface, causing scratches.

No, D A M does not have any ammonia or other strong chemicals that could attack or shorten the life of any plastic. D A M has a very small amount of alcohol (less than .3%) in a water based solution. The quantity is so small that it has no effect on plastic or other surfaces. D A M is safe on all surfaces.