A hairnet appears and disappears on Kelinda.
When Kirk is fighting Rojan (right after McCoy and Spock push him back into the room), he gets Rojan in a double arm-lock. But when the camera angle changes, he's suddenly got him in a neck hold instead.
The part in Rojan's hair changes from left to right and back. It is changed only in the face-on shot a minute or so before the end.
When Kirk gets paralyzed (when they first escape the cave), the wide shot has his arms in a natural running position. In the close-up shot his arms are wide apart.
When Rojan crushes one of the cuboctahedra, his hand is covered in a fine white powder and he drops it to the ground. The next moment his hand is clean and completely free of the powder.
When Spock goes into his 'rest trance', Dr. McCoy checks for a pulse, and indicates his heartbeat really is slow, and that the pulse is almost non-existent. In The Omega Glory (1968), it is established that Spock has no audible heartbeat, although it is also established that a normal Vulcan pulse is rapid. It is also well known that is Spock's heart is located where a human's liver is.
Rojan explains to the landing party that his neural field technology paralyzed their voluntary muscles, which held them still until they could be disarmed. However, moments before, as Rojan was making his initial demands, Kirk's eyes were darting back and forth, quite voluntarily. Rojan was presumably referring to skeletal (locomotor) muscles.
When the Kelvans reduce the crew members to cuboctahedra, their clothes are reduced with them. But items that they are holding (clipboards, pens, etc.) are not, and land beside the cuboctahedra. Since this is an imaginary technology, we just have to accept whatever we are shown regarding this matter.
In the first scene Rojan's makeup shows him as very pale and with very delineated lips, eyes and eyebrows. In the middle act when they are on the Enterprise, it now appears Rojan has gotten a nice tan and the rest of his face appears more like a 'normal' human. It could be that being around humans gave him "reference" for improved shape shifting.
When the Enterprise is approaching the Andromeda Galaxy (M31), the galaxy is seen from the same viewing angle as seen from Earth. It is unlikely that the Enterprise would be approaching in a line of sight direction from Earth after traveling several years in space. However, given the distance from Earth to the Andromeda Galaxy (over 2 1/2 million light years), the orientation of the Andromeda Galaxy relative to any point in the Milky Way Galaxy would appear to be nearly the same. Any difference in the angle from one end of the Milky Way Galaxy (approximately 100,000 light years across) to the other would be extremely small, and the Andromeda Galaxy would appear to be the same. To scale, if the Milky Way Galaxy were 1 inch across, the Andromeda Galaxy would be 25 inches away.
After Kirk's struggle with Rojan, a dark smudge appears on Kirk's sleeve (probably makeup from Rojan).
When the members of the landing party are frozen by Rojan's neural field, Kirk's eyes react to the events around him.
After Spock tells Rojan that contrary to his orders Kelinda is talking to Kirk, when Rojan storms into the turbolift he heads towards the left side of it without slowing down in the least, showing that there isn't a wall there in reality.
While Scott and Tomar are drinking various liquors, Scott tosses an empty bottle to the floor off-camera and the sound of it breaking is heard. Later, when Scott passes out, the discarded bottle is at his feet, intact.
Before Drea starts to neutralize three crew members on the bridge, one of them can be seen holding a clipboard. After Drea neutralizes them, the clip board can be seen on the floor. However, there should have been the sound of the clipboard hitting the floor, since there was no one to hold it.
The Andromeda Galaxy is treated as if it were only a short jaunt from Federation space. As Andromeda galaxy is located about 2.5 millions lights-years from Milky Way, traveling to it in 300 years would require a 20.3 warp factor speed, according to Trek's own rules.
It's never explained how the Enterprise will avoid the negative energy field that destroyed the Kelvan's spacecraft when they tried to enter the Milky Way galaxy.
As previously noted, warp 11 is not fast enough to get to Andromeda in 300 years. Nevertheless, the ability to travel at warp 11 for an extended period would have been extremely useful and valuable, yet no further mention is made of this newfound ability in the series.