Trying to remember the recorded message, Lucy mistakes the word 'embassy' for 'NBC'. Although Lucille Ball was a long-time CBS TV star, she briefly 'moved' to NBC in 1980. Although her final series "Life With Lucy" was produced and distributed by CBS, it actually aired on ABC, meaning Lucille Ball was seen on all three of the major networks.
Writer Robert O'Brien pays homage to the source material for this episode's spoof in the names given the two IM Force agents. Geller is named for Bruce Geller, the creator of Mission: Impossible (1966), and Johnson is named for Bob Johnson, the actor who provided the "mystery voice" heard on each week's self-destructing tape.
Lucy's impersonation of a Middle Eastern Maharani is a direct homage to "I Love Lucy's" "The Publicity Agent" (S1;E32) where Lucy Ricardo created the character of the Scheherazade of Franistan. Even the nasal voice is similar. Lucy Ricardo initially suggests calling the character a Maharani, but Ethel informs her that a Maharani is a Maharaja's wife, so they settle on Maharincess, combining Maharani with Princess.
Lucille Ball wears the same light blue tweed suit she wore in the previous episode, "Lucy, the Conclusion Jumper" (S1;E5).
"Mission: Impossible" was green-lit by the president of Desilu, Lucille Ball.