Find the Monkees (a.k.a. The Audition) - S1-E19
Trivia: When Mike is looking on the board for Hubbell Benson, other names that are on the board include James Frawley (another Monkee episode director), Richard Nunis (the director of the episode) and Jack Williams (a worker on the show).
Trivia: Davy is asked for a "recent picture" and produces a baby picture, presumably of himself. The same picture was used in season 3, episode 5 of Leave It To Beaver, titled "Baby Picture"; only this time it's Beaver's baby picture.
Dance, Monkees, Dance - S1-E14
Trivia: The woman with the red hair who dances with Mike, when the Monkees are pretending to be the Smoothies, is in fact his mother.
The Spy Who Came in From the Cool - S1-E5
Trivia: The knock out dance number was latter repeated on another show as they did a new dance called "The Karate" with more dancers, but was edited out and replaced with a music number.
Answer: The Monkees TV series was very much a fantasy (this was the "groovy" psychedelic 60s, after all). Impossible things, such as items appearing out of nowhere, happened on their show without explanation all the time.
Jean G