Continuity mistake: When Davy is telling Mike and Peter that Otto and Sigmund are trying to kill Bettina, the sandwich Mike has switches from his left hand to his right hand in a split second.
Continuity mistake: When David is telling Michael and Peter about the plot to kill Bettina, Peter's hair swaps between a middle parting (in the wide shots of David, Michael and him) and a side parting (in the closeup of just him and Michael).
The Spy Who Came in From the Cool - S1-E5
Continuity mistake: In the karate dance number there is a girl in a red outfit behind Mike on the floor. She must change her position at least four times in ten seconds - she can be seen moving and laughing with the girl beside her on the floor.
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.
Don't Look a Gift Horse in the Mouth (a.k.a. Gift Horse) - S1-E8
Continuity mistake: When the landlord is banging at the apartment door, his cardigan changes from blue to brown, and from unbuttoned to buttoned. (00:04:15)
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.
I've Got A Little Song Here - S1-E12
Continuity mistake: When the others are cheering up Mike, there is nothing on the side. But a split second after Davy has left the room, the pad phone suddenly appears on the side so that Micky can call Bernard Class disguised as 'M.D'.
The Case of the Missing Monkee - S1-E17
Other mistake: When Peter is tied up at the Remington Clinic, as the camera does a pan from behind him, you can see that he has been tied with a quick-release knot.
Find the Monkees (a.k.a. The Audition) - S1-E19
Continuity mistake: Trying to get away from the Monkees, television producer Hubbell Benson enters an elevator on the first floor. After a quick cut, Benson is shown exiting the elevator on the third floor. A potted plant and a "3rd Floor" sign were added to the scene but it is obvious the elevator is still on the first floor. A large ash tray appears in both shots and its contents are unchanged.
The Prince and the Paupers - S1-E21
Continuity mistake: When the Monkees (excluding David) and Ludlow come out of the cupboard that they hid in when Wendy Forsythe came to visit, you can see some items in there on shelves and neatly stacked. When David (as Ludlow) and Michael accidentally open the door a bit later (thinking they're going into a different room), they get covered in the items as soon as they open the door. Plus some of the items that fall on them were not even in there before.
Continuity mistake: When the Monkees sit down at the table in the Chinese restaurant in the end tag sequence, Peter has a watch on his left wrist which disappears in the close-ups of him, but appears in other shots.
The Monkees Get Out More Dirt - S1-E29
Audio problem: When Micky says "Ah, my aunt!", the audio starts half a second before Micky opens his mouth.
Continuity mistake: As Davy talks with Paw and Ella Mae, two dirt smudges on his right cheek keep disappearing and reappearing.
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.
Continuity mistake: After Micky has just taken apart the Klutzmobile engine and the Baron has run over to the periscope, in the next scene, Micky has magically been re-tied in a chair, even though neither Wolfgang nor the Baron tied him up again.
Visible crew/equipment: After Micky and Crumpets have been kidnapped, the amount and the slackness of the rope around Micky changes between the close-up and wide shots.
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