Many of the folds/creases can be flattened by using parchment paper on top of the crease on an ironing board with an iron. Different magazines have a variety of paper so practice heat levels on similar pages of that particular issue.
I discovered parchment paper ironing when making large water filled play mats from 6 mill construction polyurethane .
You can close up small staple holes by using a dull butter knife or lino knife and starting a half inch or so from the hole, press the smooth rounded knife edge into the surface of the paper in progressive steps toward the hole. Come in from different directions toward the hole. Go slow. practice on similar sample paper. The thicker the paper the better the response. You will discover the amount of pressure to use with each type of paper. This was a trick I learned in repairing resilient flooring seams and pin holes. I have some nice framed rag pictures that defy source.