Revealing mistake: The purple dress that Micky and Davy bring for Mrs. Weefers to wear is too big for her, showing that the dress was made specifically for Micky to wear.
Hitting the High Seas - S2-E12
Revealing mistake: When Micky is hiding in the alcove whilst the Captain is talking to his parrot, the curtain that's hiding him from view already has a tear in it before the Captain slices one in it. If you look carefully, you can see where the tear has been quickly held together with something, so that when the Captain slices at the curtain on cue, Micky just has to pull the bits apart to make it look like it's been actually sliced.
The Spy Who Came in From the Cool - S1-E5
Revealing mistake: When the female spy is taking the film off Mike who is out cold on the floor, the dancers can be seen working on the dance steps in the background. After all of the dancers have knocked themselves out they can be seen moving and laughing.
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