As Kirk, Spock, and Mitchell enter the bridge from the turbolift, a black crewman wearing a blue shirt crosses behind Yeoman Smith and has entered the turbolift by the time Kirk reaches the steps down to his chair. In the next shot, however, the same crewman is still walking toward the turbolift when Kirk reaches the same spot. In addition, Yeoman Smith is carrying some sort of cards close to her body when Kirk, Spock, and Mitchell exit the turbolift; in the next shot, the cards are gone and her arms are at her sides.
When Spock first reports on the information from the Valiant's buoy, he states that the tapes are burned out, and that he is going to begin reading the memory banks (electronic). Then a minute later, he states that he's having trouble reading the tapes.
There is a struggle with Mitchell before is made unconscious and it is obvious that he doesn't have an undershirt on. For the rest of the show, he - and his stunt double - are seen to have an undershirt.
When Kirk, Spock and Mitchell first arrive on the bridge, Mitchell relieves the navigator who then walks between Kirk and Yeoman Smith. In the next shot he has disappeared.
After the initial attack Kirk states that without Warp Drive they are now years not days away from human colonies. The difference would be 10's to 100's of thousand's of years, going from many times the speed of light to sub-light speed.
This script for "Where No Man Has Gone Before" was written in 1965, at a time when ESP was seriously believed to be an actual phenomenon. However, many comprehensive studies since then have failed to show that there are people who possess ESP. It is now commonly viewed as a pseudoscience, along with remote viewing and telepathy.
Delta Vega has a "lithium cracking station" on it. Cracking here must refer to cracking larger crystals into smaller ones.
The events of this adventure obviously occur significantly earlier than the bulk of the rest of the series. As such, the educational title of physicist that is given to Sulu is in line with subsequent appearances where he is later promoted to the positional title of, and referred to as a 'helmsman'. The same applies to Spock's different rank and uniform color as well.
(at around 40 mins) The solid rock "bounces" under Kirk's weight as he inches along the rock face just before the small boulder rolls off and crashes.
During the final fight scene its clear that stunt doubles are used for both Kirk and Mitchell.
Mitchell is unconscious when he is put on the transporter pad standing up, but he doesn't fall.
When Kirk and Spock are about to take the elevator to the bridge, an overhead view of the entrance to the lift is seen where the floor of the lift and the deck of the corridor are obviously continuous.
When looking at Dr. Elizabeth Dehner's (Sally Kellerman) profile, she is listed at 5'2", while Lt. Cmdr. Gary Mitchell (Gary Lockwood) is 5'9". When they stand next to each other though, they are close in height. Sally Kellerman is actually 5'10" and Gary Lockwood 6'0 1/2".
As erratic as rank stripes were in the series, they are outright incomprehensible here. Kirk, as captain, wears two stripes. Everyone else wears one, regardless of rank or position.
In Sickbay, when Mitchell makes himself "die", Dehner says he was dead for nearly 22 seconds. It was actually only 17 seconds.
The computer files which Mitchell speed-reads do not resemble any other views of the Enterprise computer in this series. They look very much like ordinary 1960s projector slides, completely out of place in the 23rd century.
(at around 40 minutes) you can see hands pushing the boulder towards Kirk as he inches atop the bouncing rock.
Lee Kelso's wristwatch is visible under his uniform sleeve at 4 minutes 3 second.
When Kirk fires his phaser rifle at the the rock, the explosive device is partially visible.
Visible wire used to raise the cable which strangles Lee Kelso.
Some form of camera rigging can be seen at the base of the navigation/helm console when the shot pulls back to Mitchell and Kelso as Dehner walks away from them.
As the Enterprise crew prepares to enter the Galactic Barrier, Kirk says to Mitchell to get ready to leave the galaxy. Even at maximum warp speed, the Enterprise would not have made it to the edge of our galaxy in such a short time. Therefore, Kirk's statement would be false. Further, in By Any Other Name (1968), Kirk tells Rojan that it would take thousands of years to reach Andromeda, the nearest galaxy to ours, at maximum warp. Then, Rojan tells Kirk that their modifications would only take 300 years to reach it. Any way you look at it, leaving the Milky Way galaxy is not possible with the technology afforded. Further, in Let That Be Your Last Battlefield (1969)(#3.15) an INTERGALACTIC treaty is mentioned.
On Delta Vega Captain Kirk says he wants someone with Mitchell and someone watching from "the dispensary". But Delta Vega is a fully automated station where the ore ships only stop "every 20 years", so it makes very little sense the station would have a dispensary.
Marooning Mitchell wouldn't have worked either. His powers had grown so exponentially that he withstood a full phaser blast to the chest, swept aside his imprisoning force field, and created matter out of nothing (the oasis and Kirk's headstone.) What would have prevented Mitchell from escaping the planet? His powers would continue to grow and creating a means of escape would be nothing. He could make a spacecraft appear out of thin air. Also, it is never stated whether or not if his powers have a range. What would have prevented him from reaching out into space and destroying the Enterprise? By the time Kirk finally confronted Mitchell, it seemed as though there was virtually nothing beyond his capability.
On one of the occasions when Kirk and Mitchell are discussing Mitchell's ESP powers (right before Spock and the rest of the crew enter the room), the shadow of a boom mic can be seen on the wall.
Just before Kirk and Spock stun Mitchell (just prior to beaming down to the planet), the shadow of the boom mic is clearly visible well within the frame, moving across the wall behind Spock as Mitchell gets out of bed.
Gary Mitchell makes Captain Kirk's "headstone" which reads: "James R. Kirk." In all other Trek references, his name is "James Tiberius Kirk".
In the last scene as the camera pans across the bridge the crewman seated at the communication console appears to be face down and asleep at his station.
When the Enterprise officers are in the boardroom discussing the increase in Gary's ESP abilities, Sulu uses the word "geometric" instead of "exponential". While both refer to growth rates of a mathematical function proportional to the function's current value, "geometric" refers to a function with discrete domain values; "exponential" refers to a continuous domain value. (Sulu's description of starting with a penny and doubling it daily is correctly geometric, but Mitchell's ESP was continually growing, so exponential would be more appropriate.)
During the chess game in the beginning, Spock mentioned that one of his ancestors married a human once. Although technically correct, as later on his mother is revealed to be human, it would be illogical to mention it in this way. This indicates that originally Spock wasn't written as half human, but only slightly human, perhaps 1/8 or 1/16. Just enough to irritate, as Kirk taunts Spock with it.
However, since this episode takes place much earlier than the rest of the series, it is possible that Spock had been reserved about disclosing his human ancestry and had not yet told Kirk or the crew about his immediate mother being human.
Almost the very first thing that Spock says is, "Ah, yes, one of 'your Earth' emotions." Yet, in the bridge scene, Spock is highly agitated.