It's stated that The Shadow was a "master of hypnosis" who had "the ability to cloud men's minds so they could not see him." Supposedly he learned this ability in the Far East.
I've been listening, on and off and over the years, to OTR episodes of The Shadow and I know there have been comic books, films, and pulp magazine stories and novels about The Shadow.
I would think, with the powerful hypnosis (or whatever it turned out to be) that he used to keep himself from being seen, he would be able to do other things as well. Is it ever stated, shown, or implied that he has other abilities besides clouding men's minds? For instance, has he been able to influence people so they see things that aren't there or hear something they didn't?