After T'Pau's bearers set her chair on the ground, she raises her hand, making the Vulcan salute to Spock. At first she is not wearing a ring, while in subsequent shots a ring is clearly visible.
When the wide view of Spock moving toward the gong is shown, his fiancée T'Pring begins to move to head him off. When the camera angle goes to a close-up of her face, it is obvious she is still standing still (notice the other Vulcan Stonn to her right), and begins to move again.
At about the 29:30 mark T'Pring is shown walking towards Spock before he strikes the gong. It then cuts to show her standing still and then beginning to walk again even though she was already in motion a moment earlier.
In Spock's room, there is a red blinking light in a bear-like holder in the background when Kirk is talking to him. After their conversation, the light no longer blinks, it is billowing smoke. A scene or two later, the blinker in the same prop blinks red and white.
Spock drops his pen onto the table in his quarters. The next shot shows Kirk holding his wrist and holding the pen.
Spock has to get to Vulcan immediately, insisting that the Enterprise bring him there. Captain Kirk is conflicted, as he has to attend a ceremony and can't stop at both planets in time. At no point does anyone suggest another starship or shuttle take Spock to Vulcan. However, shuttles are not designed for long-distance voyages, and it's quite possible there are no other starships in the vicinity.
After T'Pring chooses Kirk to be her champion, Kirk and McCoy are speaking with T'Pau. If you look in the background, you will see Leonard Nimoy standing against the wall with his hands behind his back, apparently unaware that he is on camera. Spock is supposed to be off in the corner, deep in the blood fever.
In the establishing shot of the arena, the beam from an overhead light becomes visible as the camera pans left.
The communication monitors in Spock's quarters, Kirk's quarters, and sick bay, all have a distinctive stain on the right bezel, showing reuse of a prop. The same prop is seen in multiple contexts in The Corbomite Maneuver (1966).
As Dr. McCoy bends down to check on Captain Kirk during the Captain's battle with Mr. Spock, the Doctor is preparing to give Kirk a shot. After McCoy gives the Captain the shot in his right arm the doctor pulls his hands away and you can see "blood" on McCoy's left hand. And while there is blood on Kirk's chest from the battle, McCoy's left hand never comes in contact with Kirk's chest.
Obvious doubles for Kirk and Spock in the climax fight.
Spock indicates he had hoped to be spared the Vulcan mating drives. Given his age, however, he would have already experienced them, as shown in Star Trek III: The Search for Spock (1984).
In the introduction, Spock requests a leave of absence on Vulcan, with a loss of only 2.8 light-days. In this context, he is using light-days as a measurement of time. It is, however, a unit of distance - 25,920,000,000 kilometers.
Councilwoman T'Pau makes many grammatical mistakes with the word "thee," when "thou" would be the correct pronoun.
T'Pau does the Live Long And Prosper hand gesture with her left hand, while all other Vulcans do it with the right. (Of course, it's possible that high-ranking female Vulcans might use their left hand for this salute.)
On his first appearance Checkov pronounces Vulcan as "Wulcan", the "V" sound is used in Russian so he should pronounce it as an English speaking person would say it. Checkov would continue to mispronounce such words.