On the DVD commentary, Michael Shannon and the director, Jeff Nichols, both clarify that the daughter was not supposed to have been born deaf but had become deaf a few years before the events of the movie due to an illness like meningitis.
The drilling rig, used by Curtis and Dewart, displays the name of an actual drilling company, "McKay and Gould" of Darlington, PA; just outside East Palestine, OH, approximately 60 miles SE of two of the three filming sites of Lorain and Grafton, OH.
The trivia items below may give away important plot points.
As it is mentioned in the DVD special features, the extras in the group lunch at the Lion's Club were only told they would get free lunch and be in a movie. They had no idea the scene would escalate to a physical fight and (seemingly) psychotic rant.
The scene where Michael Shannon witnesses all the furniture in his living room lift up spontaneously was entirely CGI. The Strause brothers and their firm Hydraulx came on board at an early stage in development; indeed they are executive producers on the film. The brothers claim that this one scene features more CGI work than any one scene in Avatar (2009).