The most obvious example is the angel itself; human beings do not have wings of any sort, and for a human to have large wings that eventually prove capable of flight is itself a magical thing. Not even the most advanced surgical skills could transplant wings onto a human without rejection, infection, and probably death. The fact of the angel's existence is itself magical because it is so far outside the realm of possibility, and the flight at the end, although played for humor, is truly extraordinary. However, the angel is also very real:
...seen close up he was much too human: he had an unbearable smell of the outdoors, the back side of his wings was strewn with parasites and his main feathers had been mistreated by terrestrial winds...
(Márquez, "A Very Old Man with Enormous Wings," salvoblue.homestead.com)
All these attributes would be seen on a man with wings, since they can be observed on birds; fleas and other parasites love birds, since they can sit under the feathers and are difficult to remove. Feathers fall out, they are ungainly, and they are hard to clean; the angel shows all the signs of being an entirely non-spiritual man, but with wings.