The major symbol(s) is/are the wings of the possible angel, and have more than one interpretation. Rather than being a beautiful being of light and spirituality, the angel is old and dirty, and his wings are missing feathers and full of parasites. His wings are not those of a holy being but of a working biology; even the doctor, seeing how perfectly the wings fit in with the angel's body, wonders why wings aren't more common. The angel's specific wings are the focus of attention, as a different flying person is ignored:
A traveling carnival arrived with a flying acrobat who buzzed over the crowd several times, but no one paid any attention to him because his wings were not those of an angel but, rather, those of a sidereal bat.
(Márquez, "A Very Old Man with Enormous Wings," salvoblue.homestead.com)
The wings should represent the existence of a spiritual world with creatures beyond human comprehension, but instead they are utilitarian and plain. The symbolism, instead, is of the amazing things that exist in the real world that need no supernatural explanation; the "angel" has wings because his race of humans has wings, and they serve a useful purpose instead of a spiritual symbolism. When he flies off at the end of the story, he is using his wings as they are meant to be used, not as the town used them: to gawk and jeer, as an excuse for good or bad fortune, or to distract them from everyday life. The wings are a symbol of Man's natural abilities, and when these abilities are seen as unusual, they are mocked and cast out, but when the abilities are used for their intended purpose, no one can call them unusual anymore.