The title of the film refers to folklore about subterranean ghosts or creatures who are believed to menace miners. The 'Tommyknockers' of the film are, of course, the possessive alien spirits inside the buried spacecraft.
When Sheriff Ruth Merrill is searching in the woods for Davey Brown, she is accosted by Bobbi Anderson's dog. She remarks that he is acting like a "Cujo." This is a reference to the Stephen King novel turned film of the same name.