When Spock and Kirk enter the master computer room, there is a wall behind them about 5'-10' away and no robots. The camera cuts away to the master computer for a second or two, then cuts back to Kirk and Spock and now three robots have appeared between them and the wall. In the next longer shot, the two men are standing in the middle of the room, the robots are behind them, but there's no sign of the wall.
When Uhura is singing by the lake, her reflection in the water doesn't show her uniform rank on her sleeves.
Towards the end of the episode, we see the crew use seat belts. During the original era the Enterprise never before (or since) had seat belts on chairs.
Sulu is shown erroneously sitting on the bridge while he was actually imperiled on the planet's surface.
On the bridge, McCoy's tricorder strap briefly disappears and reappears.
The hangar doors open to the side in this episode, as opposed to from the center like a clam as seen on the original series and later in "Albatross."
Several crew wearing red uniforms have the science (blue uniform) insignia on them.
Spock: The Queen of Hearts and her cards are characters from Alice Through the Looking Glass, Captain.
Kirk: I read the book as a child, Mr. Spock, but I wasn't aware you indulged in the literature of fantasy.
Spock: Light reading is considered relaxing, Captain. My mother was particularly fond of Lewis Carroll's work.
Amusement Park Computer: Unfortunately, I have no use for more hostages which leaves me no choice but to turn them off.
Uhura: Turn them off?
Amusement Park Computer: Again redundant. I will make them cease to function. I will turn them off.
Uhura: That's murder.
Amusement Park Computer: That is a word meaning to cease to function?
Uhura: Yes, but...
Amusement Park Computer: Good. It is as I wish. I will turn them off.
Spock: Our amusement park seems no longer content to amuse.
Uhura: There is no shame in serving others when one does it of his own free will.
This episode along with "The Eye of the Beholder" was released on The Animated Adventures of Gene Roddenberry's Star Trek: Volume 8 for VHS.
An accomplished singer, Nichelle Nichols as Lieutenant Uhura, sang in this episode as she had done in a number of original Star Trek episodes. In this episode, she vocalized for almost 40 seconds
Trivia: In this episode, the date of the Caretaker's death could be read off of the gravestone: "7009th year of operation."
A scene in this episode showed the interior of the Enterprise hanger deck. Visible in the hangar deck was a heavy shuttle (as seen in "Mudd's Passion"), and a long range shuttle (as seen in "The Slaver Weapon").
A direct sequel to the Original Trek episode "Shore Leave", and there are references to McCoy's encounter with the White Rabbit and the Keeper from that episode.
Alice and the White Rabbit
These characters following it are from the novel Alice's Adventures in Wonderland (written by Lewis Carroll). Later, McCoy is attacked by playing cards--these are from the sequel, "Through The Looking Glass". The rabbit and Alice also appeared in the Original Series episode, "Shore Leave," that first showcased the so-called shore leave planet.