After Fargo explains that S.A.R.A.H. once used to be a war games simulation program, S.A.R.A.H. asks, "Shall we play a game?" This is the same thing W.O.P.R. says to David Lightman (mistakenly believing that he is Prof. Falken) in WarGames (1983).
There are several references to 2001: A Space Odyssey (1968): After various town residents have been invited to see Jack, he tells them all to get out. At the command, "S.A.R.A.H., door!" S.A.R.A.H. replies, "I'm sorry, Jack. I'm afraid I can't do that right now." This is a word-for-word quote (except for the name Jack) to another computer who runs a "residence" - HAL. S.A.R.A.H. also says "Nathan? What are you doing, Nathan?" This is a "2001" quote, replacing "Dave" with "Nathan." Fargo says that S.A.R.A.H. has "gone all HAL on us," another obvious reference.
The power source of the Sheriff's home, a Radioisotope Thermal Generator, is a real device. They're used mostly in remote locations removed from power grids and space probes.
Jo's ringtone is the first six notes of the US National Anthem.
The pizza box that the delivery guy is carrying has numbers all around the outside of the box. These numbers are some of the digits of pi. This is because the pizza place has the symbol for pi in the name, which means the name is pronounced "pizza pi", or "pizza pie".