Big News from Wikipedia. The theme music for the old sci-fi sitcom “My Favorite Martian” was performed on an electro-theremin by Paul Tanner, a former member of Glenn Miller's band. That spooky sound persuaded Brian Wilson to ask Tanner to work with the Beach Boys on "Good Vibrations."
Meanwhile, in the episodes themselves, I always noticed a painting hanging on the wall of the main apartment set. In my surreal imagination, I assumed the painting showed some sort of mutant kiwi bird with a trunk, pecking across the sands of Mars.
For better or worse, the internet has set me straight. It was a normal bull, upside down; in a reproduction of an 1801 woodblock print by Sawa Sekkyo. Thanks to J.H. Harison on her site http://members.tripod.com/~jhh_2/TVMFM.htm