Warren says to Jack, "what were you expecting, the Spanish Inquisition?" Jack replied: "No one expects the Spanish Inquisition." Both paraphrasing the call and response of the famous Monty Python Flying Circus (22 Sep, 1970) skit of the same name.
The title, This One Time at Space Camp, is a play on the line "this one time, at band camp..." which was spoken by character Michelle Flaherty, played by Alyson Hannigan, in the film American Pie (1999). The original version of the line ended with a shockingly raunchy story from an apparent girl-next-door type.
In a blink-and-you-miss scene, when the Awesome Possum Team approaches the Radical Raccoons Team to taunt them, one of the diagrams pinned on the board appearing in background next to young Fargo is titled POSSUM KAI, obviously another nod to The Karate Kid rivalries.
Fargo, Parrish, and Holly Marten all attended Galaxy Camp.
Aaron Douglas, who plays Dr. Ray Darlton, a rocket engineer in this episode, also played Chief Tyrol, a rocket powered fighter engineer, on Battlestar Galactica.