When Finch activates the robot he reminds him of his four prime directives. The first is Isaac Asimov's first law of robotics.
Finch's small robot is named Dewey in a nod to the robots Huey, Louie and Dewey in Silent Running (1972). In Silent Running a man is left alone with only the company of his robots and teaches Dewey how to look after the plants in the garden on a spaceship.
One of Finch's books is titled "Apocalypse Survival" and is dated 2028.
Jeff the robot was animated using motion capture technology.
The company "tae technologies", whose name and logo are shown throughout the film, is an actual company working to create fusion power. They are, however, based in California rather than St. Louis.