In the overhead shot when Sulu is about to activate a Rec Room program, Nurse Chapel is seen in place of Lt. Uhura.
After McCoy enters the holodeck rec room, a black strap appears and disappears on his left shoulder. It can be seen when Sulu brings up the beach simulation, when they enter the forest, and later when he goes to the bridge after escaping the rec room.
Somehow the computer manages to create a pit in the rec room. There's no indication that they would go to the effort and expense of making the holodeck multi-floored just so someone can experience a simulation with a pit. Nor is there any indication the three officers walk up any kind of slope.
How could a hot air balloon fly in space and in a straight line. And if a balloon were hit by a Romulan plasma energy torpedo wouldn't it vaporize instead of just popping--what was it made out of? (editor's note: clearly the casual reference to the decoy as a "hot air balloon" is a simplification of a much more complex phenomena. The novelization by Allan Dean Foster sheds some light on this.)
When the three Romulans move in to attack the balloon, the top-most ship is pointed in the direction they're moving: toward the upper-right corner of the screen. The middle ship is facing toward the camera, and the bottom ship is pointed toward the lower-left corner. Despite that, all three ships move toward the upper-left.
During the second Romulan attack near the end, the stars are missing from the lower right 2/3 of the view. Only the top left 1/3 has even a sparse population of starfields.
Spock: Amazing. This deck is covered with ice.
Kirk: And it was almost covered with us.
Spock: Question; why are we unable to communicate with crew members McCoy, Sulu and Uhura?
Computer Voice: Answer; that is for me to know and for you to find out.
Kirk: Did I hear that right?
Spock: Affirmative. The dysfunction is more severe than I thought. Question; are you deliberately holding our missing crew members prisoner?
Computer Voice: I'll never tell.
Kirk: Let me try. This is Captain James T. Kirk speaking. You are programmed to obey any direct order I may give, correct?
Computer Voice: Correct.
Kirk: Very well, I order you to release McCoy, Sulu and Uhura immediately.
Computer Voice: Say "please."
Kirk: Well, I'll be...
Spock: I suggest compliance, Captain.
Kirk: (through clenched teeth) Please.
Computer Voice: Say "pretty please... with sugar on top."
Romulan Commander: Turn off those food synthesizers! We're knee-deep in deserts and they're still pouring out!
McCoy: Shall we tell them how they can reverse the effects of the field, Jim?
Kirk: Yes. But later. Let's not spoil their fun just yet.
Majel Barrett is credited but only voices M'Ress, not Chapel.
Although the animated series is not considered canon, this constitutes in essence the first appearance of the holodeck, superseding the one in Star Trek: The Next Generation. In this episode, however, it's called the Rec Room.