Archer refers to powdered drink mixes Goofy Grape, Lefty Lemon, and Rootin'-Tootin' Raspberry. These were names of a line of drinks, similar to Kool-Aid, called Funny Face in the 1960s.
The computer that "Krieger" destroys displays a similar appearance and design to "Hal 9000" from 2001: A Space Odyssey (1968).
When Archer's laser won't work, he says, "Um, Alex, I think my buzzer's broken." This references a joke from Saturday Night Live (1975)'s Celebrity Jeopardy! (1984) skit in which Norm MacDonald (portraying Burt Reynolds) would frequently interrupt Alex Trebek to report that his buzzer had broken.