When Kirk and the crew run for shelter at Reger's house, they enter a door which has windows and curtains. But in the very next scene of them inside, the doors are completely different with no windows.
When the landing party is talking to the locals, they point to a clock that reads about 2 minutes before 6. 30 seconds later, it chimes and the festival starts.
When the landing party ducks into Tamar's house during the festival, it is broad daylight. However a few minutes later when Tamar shows them to their room it is completely dark outside. Additionally, when Kirk looks out the window later, he can clearly see the scene outside where the street is well-illuminated by the street lighting; however, the earlier shot from inside the room shows complete blackness out the window.
In the dungeon, when McCoy accuses the rest of the crew of not being "of the body" he grabs Kirk around the neck, at which time Kirk also grabs McCoy around the neck. When the view shifts to see McCoy's face, Kirk's hands are no longer around McCoy's neck. When the scene shifts again to Kirk's face, you see his hands rising again to go around McCoy's throat.
During Kirk's final star-log entry, we cut from a shot of the view-screen to an opposite viewpoint and see Kirk standing in front of the helm, whereas in the previous shot he wasn't there.
When Landru first appears in the hiding place, one of the background extras starts to cover his ears, mistaking the sound of the holographic Landru appearing for the crippling ultrasonic waves that would occur towards the end of the scene. You can see his fellow extra correcting his missed cue.
When Kirk's landing party are running from falling rocks, one of the rocks bounces off the head of a crewman.
After the away-team discover the stunned Lieutenant O'Neil, one of them nearly stumbles over the extended foot of a "stunned" woman who adjusts her foot for him.
Many of the characters are wearing white collars in this episode, and make-up stains are noticeable on them.
After the computer 'Landru' self-destructs, it seems that Lieutenant Sulu is 'back to normal', in uniform, and ready to resume his duties rather quickly - instantaneously, in fact.
The crew just beamed down in the town. There is a wide shot of the street. There are Electric or phone poles in the background, rising above, beyond the buildings. Yet when they are taken to the room where they will stay, their host lights a gaslight.
When Kirk is trying to wake everyone in the dungeon, the shadow of the camera is very visible as it passes a stone wall between the camera and Kirk.
In the teaser, Sulu is absorbed by a Lawgiver simply touching him with his staff. It is unclear why the members of the follow-up landing party have to be taken to an absorption chamber.
It is never explained why Landru's "perfect" society needs the Red Hour. The purpose of this Festival is never explained, nor is the event ever mentioned after the first few scenes.
It is never explained why some characters are 'immune to absorption', even though there are enough of them to have formed an underground resistance movement. As a science officer, Spock should logically have questioned this, as it could have been the key to defeating Landru.
It is not explained why O'Neil wasn't beamed aboard at the same time as Sulu, when the transporter room was told to beam them both up. Even though O'Neil had run from the Archon that was approaching, the transporter would have beamed him up using his communicator. If the communicator had been dropped, it would have been beamed up without O'Neil.
In the initial set-up of the story, Sulu calls the Enterprise and asks for an emergency beam-up. Why did he not just use the emergency signal as used in Tomorrow Is Yesterday (1967)?
The pronunciation of 'Landru' varies between characters and scenes, with some characters using multiple different pronunciations within the same conversation. Given the use of mind control on Landru's subjects, there ought to be no variation.
Kirk seems overly impressed with the projected image of Landru while in Reger's safe place. Spock tells Kirk it's a projection, and Kirk seems amazed that there is no receiving apparatus at their location. However, Kirk's own transporter aboard his ship can transmit matter and even living things across vast distances with no apparatus at the receiving end.