In the original series, ship and bases had different chest insignia. The insignia for a starbase is a sunburst pattern (as seen on the commodore), while starships use a delta pattern (as seen on Enterprise crew). When the four officers leave the commodore's office in the teaser, the receptionist just outside stands to attention. When she stands up, she can be seen to be wearing a delta shaped badge (indicating a starship assignment) instead of the starbase's sunburst.
When Spock takes McCoy to see Pike on the Enterprise, McCoy begins to say, "I still see you flashing no," before Pike actually starts flashing.
The closeup of Kirk, Spock and McCoy first arriving at Starbase 11 shows a low hedge to their right. This is not present on the previous matte shot where Miss Piper walks out to meet them.
When the landing party enters the transporter room, the transporter assistant is wearing glasses. After the next shot of the transporter pad he is no longer wearing the glasses. (Perhaps this crew member had a dose of Retnox 5 between shots?).
Immediately after Captain Pike is abducted by the Talosians, remaining crew members fire at what they believe at the time is the door to the elevator which appeared to be the form of transport used to take the Captain. They fire three phaser barrages at the "door," and in all three cases the exact same thing happens: particles of the portal are blasted out, and the entryway is damaged but in perfectly identical fashion. Update: This could also be explained as an illusion created by the Talosians - they would have been quite capable of making the crew see the same destruction, yet believe that it was new and different each time. As they find out later, they did indeed succeed in blowing the top of the elevator system off, but the Talosians created the illusion that they had not done so.
In an Article 32 hearing, if a defendant pleads guilty of charges, the court would proceed to directly to sentencing and would have no need to present evidence. Only with a not guilty plea would evidence from both defendant and prosecution be presented before the court.
Each of the crew in the landing party on Talos IV casts multiple shadows due to multiple studio lights. In a double-star system, the two stars could be in very different parts of the sky, not positioned so as to create shadows in such different directions.)even on the other side of the planet, so multiple shadows are perfectly feasible.
On Talas IV Spock touches the blue vibrating leaves and smiles at Captain Pike. Vulcans don't normally smile, certainly not with the wide grin that Spock displays here. However, Spock is half-human, trying to fit in with a human crew.
Captain Pike's quarters has a porthole in it. There are no decks large enough to contain the corridor outside his quarters with corresponding portholes in them.
At the hospital, Kirk, McCoy, and Mendez mourn that Pike's mind is healthy, but his crippled body has no way to communicate with others, except for the yes-no flashing light. Have they forgotten Spock's power to mind-meld?
It's stated that there was no way to communicate with Captain Pike, but the fact that he was able to signal with his wheelchair shows that a means of communication using Morse Code or some other system making use of the wheelchair's capability could have been developed.
When Spock slows down the Enterprise to pick up Capt. Kirk in the shuttle, he makes no mention of Commodore Mendez. Yet, later he is transported to the ship and Spock talks to him during the trial only to find out later that he wasn't real.
The 23rd century has talking computers. Capt. Pike's wheelchair could have been equipped with a talking computer to give him the ability to speak.
After Spock steals the Enterprise Kirk attempts to follow it in a shuttlecraft, however shuttles in the mid-23rd century did not have warp drive, only impulse engines, their top speed was only 0.5c; it wasn't until the early 24th century that warp cores small enough for a shuttle were able to be made. Spock mentioned Talos IV was six days away at maximum warp, meaning the Enterprise was traveling at a velocity of warp factor 8, it would have been futile to try and follow them in a shuttle.
Just before their first visit with the injured Capt. Pike, Commodore Mendez asks Kirk if he knows Pike. He then states that Pike was about Kirk's age. However, the plot is about an incident that happened 13 years before, when Spock was Capt. Pike's science officer. This would make Pike a 21-year-old starship captain.
Spock is referred to as a lieutenant commander, rather than his actual rank, as shown by the braids on his sleeves, of full commander.
When Captain Pike and Dr. Boyce meet in Pike's cabin, Pike clearly says: "Unless we get anything more positive on it, it seems to me the condition of our own crew takes precedent." "Precedent" is used incorrectly. The word should have been "precedence".
McCoy bemoans that medicine has figured out how to tie into every organ in the human body except for one: the brain. But they have tied into Pike's brain. He is able to manipulate his wheelchair, to move it and to blink the light on the front of it, using his brainwaves. The technology to interact with the human brain clearly exists, even if it is crude and unrefined.
When Spock turns himself over to McCoy for court martial, he temporarily places Mr. Hansen in command of the ship. Mr. Scott is shown to be aboard. As second officer, he should have been given command.