In all honesty, I am not sure I would consider him the anti hero.  I think that Shiva plays this role much better in the novel.  Perhaps, we could try to reconfigure Saleem as an atypical protagonist.  If this could be the case, I would propose that one reason he can be seen in this light is that he lacks the qualities of the heroic protagonist.  Rushdie creates a character that is supposed to be the champion of Modern India.  Deliberately, he makes him awkward around women, possessing a runny nose, and a heroic quality of having a strong sense of smell.  His attempts to be a "hero" don't exactly work out for the best, as seen with his attempts at organizing the Conference of Midnight's Children and his desire to protect Parvati.  In the end, he is a symbol of endurance, one whose talents and aspirations lead him to work in a spicy pickle factory.  One has to search for the traditional definition of a hero in this capacity.