(at around 26 mins) The two boys are walking through the woods where the spaceship is and the one boy tells the other, his mom told him that this is where the Mic - Mac Indians used to be. The Mic Mac Indians are also mentioned in Steven Kings film, The Pet Cemetery, where they buried the dead.
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.