In the episode "The Phantom Voice" (February 6, 1938) a crooked lawyer and his henchman figure out a way to catch the "invisible" Shadow! The Shadow has gone to the office of lawyer Anthony Vogel to try and solve a crime that Vogel is involved in. Vogel is talking with his henchman, Travers, when The Shadow makes his presence known - although he has clouded Vogel's and Travers' minds so they cannot see him.
Vogel gets an idea! Although The Shadow can't be seen physically, he is still physically in the room and they can get their hands on him. Vogel and Travers stretch their arms out and walk slowly across the office and sure enough - Travers gets his hands on The Shadow and begins to wrestle with him! (I won't spoil the episode to tell you what happens next, so give it a listen to find out!)
I thought this was a pretty ingenious idea on the part of the shyster lawyer Anthony Vogel. It took advantage of the one flaw The Shadow has - he is still physically present although he can't be seen.