Many people confuse the pretty indentations left by rope, with rope burns. A rope burn is when the rope is pulled across the skin so fast that it either removes skin, or the friction literally causes a burn. You need to appreciate how this happens so you can avoid it.
Pull the rope across your own skin, a soft and sensitive area, and note how fast it has to travel before it becomes uncomfortable. You'll notice natural fibre is more forgiving that synthetic rope.
So let's look at how you reduce friction. You should take care not to trap the rope when pulling through; lift the bindings or the rope to avoid unnecessary friction and go slow.
If you want to move the rope quickly simply guide it away from the skin.
You should also watch out for the end of the rope, as if pulled through too quickly it can whip round. For some moves this is just a questions of guiding the loose ends, or slowing down as the knots are about to come free. If you're working near the face, try to use one hand to protect it; a knot in the eye is decidedly un-erotic!