After Kirk's mutated hands are shown to heal, they are again mutated in a later scene.
When Kirk and Spock first enter the Sealed Place, one shot shows two successive Kirks swimming, not Kirk and Spock.
When the Aquashuttle is submerged, its propulsion makes a high-pitched humming sound giving the impression it has some type of "water jet" drive; however, when fleeing from the ser-snake on the surface of the water, the sound effect used is that of an outboard motor. The same sound is used for the "scouter gig" but no motor is visible. It is highly doubtful that either of these 23rd century watercraft would be equipped with a 20th century internal combustion outboard motor.
As Kirk swims toward the camera with Spock (e.g. 8:55), his pants flash different colors as differently colored paint was used on some of the gels.
The animators were rather lazy when the ser-snake attacks the Aquashuttle. When the creature slams it against the rocks, a simple jagged black line is drawn over the shuttle's slightly distorted animation model. As powerful as the impact was, there would have been far more initial damage and pieces flying off.
When wrangling the sea monster for its venom, Kirk and Spock swim forward from the background toward the "camera". Their images get bigger to suggest a perspective change. But, the animators carelessly left an alien in front of them holding a net in the foreground. This makes it seem more like Kirk and Spock are enlarging behind the alien rather than approaching the viewer.
Near the end of the episode the Enterprise phasers change the direction of the planet quake to effect only the polar region, which Spock says is "totally uninhabited". But, earlier in the episode it is repeatedly established that the ship's sensors cannot detect the aquatic life forms, so the polar region could possibly have been densely populated.
It is odd that Kirk did not order the aquashuttle pilot to attempt a lift off to escape the ser-snake. This was corrected in Alan Dean Foster's adaption in his book "Star Trek Log Five." Kirk gave the order, but the shuttle's lift engines were damaged and non-functional. Why this was not in the script is unknown.
The Aquans save Kirk and Spock from drowning by changing them to water-breathers, then want nothing more to do with them. Domar says his Aquans don't believe in taking lives, but then, at the midpoint of the story, they bind Kirk and Spock to rocks above the water line to suffocate in the open air. What they say does not match what they do.