When the music player is in Spock's quarters, at one point, he is holding a pen near his mouth. In the following shot, his hands are on the desk.
Despite the Enterprise entering Romulan space, in fact 3 hours into Romulan space toward Eden, the Romulans don't even make contact, much less challenge the Enterprise as an invading ship. The warlike Romulans appear to have given the Enterprise a "Get into Romulan Space Free Card" whereas they have been quick to appear in similar situations.
Irina, a native Russian, occasionally pronounces Chekov's first name as Pavel, the way a native English speaker would, rather than as Pawel, as a Russian would. The Russian language has many dialects, so both pronunciations can be used.
In the brig, when Sevrin turns his back to the camera, the wrinkles of his bald cap are visible.
Two times, a shot of Kirk is reversed (presumably to make him face the right side of the screen) The first time he is facing Sulu in a corridor of the Enterprise, the second he is looking where Dr. Sevrin had just run on the planet Eden. Note the appearance of the Star Fleet emblem on the right side of his shirt, rather than the usual left side.
The seam of Adam's wig/bald cap can be seen separated from his skin in some scenes.
Eden is uninhabited. However, all of the acid-filled plant life is neatly arranged and the grass looks freshly mown.
Captain Kirk called for a tractor beam to capture the stolen shuttle but, in the following shot, there isn't a tractor beam on the shuttle and it continues on its erratic path before exploding.
During Adam's first song, Tongo Rad's drumming does not match the soundtrack.
As Spock is introducing the Vulcan lute to Adam, in his cabin, his finger movements do not correspond with the pitch of the played notes.
As Adam plays his guitar-like instrument, his strumming does not match the music, mainly during his first song.
In some shots, Adam's mouth movements whilst singing do not synchronize with the sound.
When the Enterprise is shown in profile moving toward Eden, bright lights can be seen passing over the ship's hull. Those lights are the ceiling-mounted studio lights reflecting off the model of the ship. This was corrected in the remastered version.
As Captain Kirk walks away from Tongo Rad after they are transported aboard, the shadow of the boom mic can be see on the back wall.
While Kirk or Spock frequently refer to past events on planet Earth, nobody ever mentions the hippie craze of the 20th century, the obvious inspiration for this story.