When Kirk looks through the viewscreen at the reduced Enterprise, a man is seated at the helm. Yet, when the shot switches to a full shot of the bridge, a woman is at the helm.
In the wide bridge shot of the "frozen" Enterprise, the crew is motionless, but the panel lights are still running. However, when the shot changes to the viewscreen, both the lights and the crew are frozen.
Rayna's name is spelled correctly on her name tag but appears in the end credits as "Reena." This has been corrected in some editions.
The robot delivers the medicine by dropping it on a corner of the table.
In the next shot, it is in the middle of the table.
When Kirk and Rayna are playing pool, she shoots and the ball does not go into the pocket. They are in fact playing Billiards.
In the first minute of the opening scene of the re-imaged version, as the digital Enterprise sails by the camera, the planet can be seen through the impulse engine port. It is a CGI oversight, where the appropriate graphic is missing and the planet imagery is bleeding through the missing picture.
At the beginning of the billiard table scene (about 14:45), there is excessive camera shake during the overhead views.
During Rayna's final speech, the viewers can see that some of her teeth are either black or blue, which would have no purpose in an android.
Flint references an outbreak of Black Death in Constantinople in 1334, but this was actually the date of the first major outbreak in China. Black Death didn't actually reach Constantinople until 1346/7.
Writer error: the platinum blond guy asks the blonde ponytailed lady "are you lonely?" to which she replies: "what is loneliness?". If she is a space alien and doesn't know the adjective, she sure as heck wouldn't know that the noun is "loneliness".
The sheet music for Flint's Johannes Brahms waltz, which we see in a close-up, does not correspond to the waltz Spock has played.
When M4 turns over the processed Ryetalyn to McCoy, the wire suspending the robot model can be clearly seen.
Flint has lived under many assumed identities, learning "to conceal [my immortality], to live some portion of a life, to pretend to age and then move on before my nature was suspected." Among the past identities of Flint are King Solomon, Alexander the Great, Leonardo Da Vinci, and Johannes Brahms. The problem with this notion is that all of these men's births and/or deaths are well documented, and not cases of someone coming out of nowhere and then fading out of history. Solomon and Alexander were royal heirs who were born in palaces, and their deaths caused turmoil and the permanent schisms of their realms. While Leonardo and Brahms were not kings, their deaths were well witnessed.
It is never explained why the landing party beamed down so far (4 km, about 2.5 mi) from the initial ryetalyn deposit. A comfortable hiking speed is two to three miles per hour, meaning it will take them about an hour to reach the deposit then time to gather the ryetalyn. It would have made better sense to beam down closer to the ryetalyn deposit or have come down in a shuttlecraft as to be more mobile on the planet's surface.
When Flint tells McCoy that M4 will process the Ryetalyn, McCoy answers back that he wants to supervise that. A moment later, M4 flies to the lab where a door closes and with a pane of frosted glass separating the two rooms. With McCoy being shut out like that and not being able to see what was going on, he should have marched out and complained to Flint.
Near the end, everyone knows that Rayna is an android. Soon she collapses from all the stress of deciding between Kirk and Flint. Dr. McCoy rushes to her and checks for a pulse. He already knows she's an android of unknown design, so checking for a pulse makes no sense at all.
When Spock first examines the artwork he describes it as "the most unique". The word "Unique" is an absolute modifier and means "unlike anything else". Words like "very", "extremely" and "most" should never be used to modify it and Spock should know this.
At the beginning, Spock says that the ship's sensors did not pick any life forms on the planet. A few minutes later Flint says that his planet is shielded from outsiders. Once inside Flint's home, Kirk communicates with Scotty on the ship and tells him to do a full scan of Flint. How is this possible if the planet is shielded and the sensors can't pick up life forms?
McCoy gives an eloquent speech saying that Spock will never know the joys and sorrows of love. This is incorrect, since Spock experienced exactly that in This Side of Paradise (1967)(#1.24), in which he was able to fall in love due to the influence of alien spores. At the end of that episode, he says wistfully that it was the first time he had ever been happy. In All Our Yesterdays (1969)(#3.23), he again falls in love due to his reversion to primitive Vulcan behavior.