Both grain ships have the same registration number, NCC 61465. Registration numbers are supposedly unique; each grain ship should have its own.
Just after Kirk in covered in a pile of tribbles, Scotty hands him another one. Between the shot of Scotty's face and the shot of his arm with Kirk, his rank changes from Commander (2 full braids) to Lt. Commander (1 full and 1 dashed braid).
When McCoy brings a tribble to the bridge, his rank insignia shows one full and one dashed braid for Lt. Commander. However in all other shots he has two full braids for Commander.
In a shot where Cyrano stands on the bridge, the doors of the turbo elevator are drawn off-center to the right.
In one scene Koloth is actually on the bridge of the Enterprise when Kirk is talking to him on his ship, instead of on the viewscreen.
M'Ress has been manning the communication station throughout the episode. However in the stock overhead bridge shots, Uhura is at Communications.
Both times, Nored is alone when she confronts the Vendorian. Standard protocol (as noted in the novelization) and common sense when dealing with a shapeshifter would be to have teams of at least two security officers at all times, to prevent a substitution.
When "McCoy" responds to Spock's question about the possibility of him making an error, Spock briefly turns a much brighter shade of orange/yellow. Later on the bridge when Spock advises surrender, the same basic shot is used and the same coloring error repeats.
When the alien renders McCoy unconscious and returns to talk to Nored, "McCoy"'s hair is briefly a much lighter shade of brown, matching Lt. Nored's.
Granted, McCoy has just been nerve-pinched and rendered unconscious, but it seems impossible that he wouldn't realize there was a third bed in sickbay. He's overhauled the equipment there, treated patients, run diagnoses on the beds... but he doesn't notice there's an extra one?
The Vendorian is capable of taking on physical forms, but there's no explanation for how it can convert itself into energy to make a deflector shield. (Alan Dean Foster attempts to explain in the novelization by saying it took on the form of replacement parts, but no such explanation is presented on-screen.)
Kirk says that there used to be only two beds in sickbay, but surely there would be more. At least there were more in the live-action series. Also, how would he know the exact layout of sickbay. For example: McCoy wouldn't know the exact layout of Main Engeneering now, would he? On the other hand Scotty would!
The insignia on Lt. Nored's uniform jumps to the opposite side in one shot as she holds a phaser on "Winston" and Kirk comes into the room.
Also in regard to the giant Spock, exactly how was Keniclius able to replicate a giant version of his uniform? It would have taken tons of the right fabrics to make an exact recreation.
The usual problems with giant-sized humanoids: as size doubles, mass squares. A giant-sized Spock or Keniclius would be too heavy for their muscles to move them.
So exactly how is a giant Spock going to be particularly useful in conquering the universe? Or even an army of giant Spocks? Even if you want an army of super-smart Spocks to help you, why make them giant-sized? That would seem to make them merely bigger targets.
After Spock is captured by Keniclius, there's a bridge shot with Spock in it before he is rescued.
The episode perpetuates the commonly held belief that witches were burned in Salem. No witches were burned in Salem or anywhere else in the U.S., although some were burned at the stake in Europe.
In this episode the Enterprise explores the center of the galaxy. In Star Trek V - The Final Frontier Kirk claims that no vessel or probe sent into the center of the galaxy has ever returned. (Note however that the Trek producers don't consider the animated series canon.)
The beginning stardate of this episode is 1254.4, which would have it set even before Star Trek's second pilot episode "Where No Man Has Gone Before" at 1312.4. In the latter, Uhura and McCoy weren't yet serving onboard the Enterprise and Sulu was the ship's physicist, and as a science officer, was wearing a blue uniform at the time.