"Moonbase Freedom" is the second of three fictional Ronald Reagan movies in this season. The clip actually shown in the theater scene is from Edgar G. Ulmer's The Man from Planet X (1951), which was indeed released in 1951.
The title comes from the philosophical book of the same name by Søren Kierkegaard. The book is Kierkegaard's attempt to explain Abraham's decision to kill his son Isaac.
The song that plays over the end credits is "Down in the Willow Garden", an Appalachian murder ballad about a man facing execution for killing his lover. It was previously featured as the lullaby that Ed sings to Nathan Jr. in the film Raising Arizona (1987), which was directed by the Coen Brothers (Joel Coen & Ethan Coen), who are also producers of this TV series.
When Ed (Jesse Plemons) and Peggy (Kirsten Dunst) are speaking with Officer Solverson (Patrick Wilson), Ed says he "slipped on some ice" which is why he's wearing a neck brace. This is the same excuse Lester Nygaard (Martin Freeman) gave in Season 1 after he was given a black eye by Sam Hess (Kevin O'Grady).