As the Earps and Doc Holliday walk four abreast to the O.K. Corral, their order changes several times, from shot to shot, with no visible change of order by the actors. It starts with Doc Holliday moving from far left to left center to far right, all shots, always four abreast, in a straight line across.
Although the OK Corral is swept by wind and flying debris in the last act, this effect ceases during the close-up shots where Spock mind-melds with the crew.
The bartender has five glasses on his tray when he comes to serve the crew drinks. After putting two on the table, it cuts to Kirk and Spock, and we hear the sound of him putting two more glasses down. But when it cuts back to the bartender, there are still two glasses on the tray.
When the man is shot after he is thrown out of the window of the saloon early in the show, his hat falls off twice.
When the bartender asks Kirk and his men whether they want the usual to drink, Sylvia is standing behind Chekov with her hands at her side. In the very next cut, she has her hands on his shoulders massaging him.
During the shootout at the OK Corral, Doc Holliday fires his double-barreled shotgun several times without reloading. However, the "inexhaustible firearm" is a common trope in Western movies, and this one is designed to be surreal.
The gunfight at the O.K. Corral, as portrayed here, has many inaccuracies, but that's because the Melkotian created the town based on Captain Kirk's imperfect recall of history. The gunfight actually ensued at 3:00 p.m., not 5:00 p.m. Virgil Earp was the town marshal of Tombstone at the time of the gunfight, not Wyatt Earp. Morgan Earp was Virgil's deputy, and Wyatt and Doc Holliday were deputized on the day of the gunfight. Their original intent was to disarm the Clantons and the McLaureys. Doc Holliday did not practice dentistry in Tombstone. Perhaps most importantly, Ike Clanton (Kirk) was not killed in the gunfight, but lived for six years afterwards and, in fact, killed Morgan Earp, and arranged to have Virgil Earp ambushed and crippled.
After realizing who they all are, a bar fight that ends with a shooting occurs. The external shots of the bar from the crew's perspective show no one in the bar. As soon as they enter, the bar is teeming with people. This adds to the intentional surrealism of the scenario.
In reality, Doc Holliday was 30 at the time of the O.K. Corral shootout. Sam Gilman played Doc Holliday when he was 53 and looked like it. This adds to the intentional surrealism of the scenario.
Dr. McCoy and Chekov's positions are reversed from the time they are standing on the alien planet to when they are transported to Tombstone. However, they have not been transported by the Enterprise but by aliens using an unknown technology, which could potentially change their position or anything else.
During the lead-up to the shootout, as the Earps are approaching the O.K. Corral, flashes of lightning cast shadows of the trees onto the "sky" showing it to be the walls of the studio.
When Morgan Earp quick draws his pistol to shoot Checkov, he does it too quickly and actually fires above Checkov's head, nowhere near his chest. (This is noticeable even though they tried to cut away just as Morgan Earp shot.)
When at the O.K. Corral, the landing party is in a line along the fence when the Earps & Doc Holliday open fire. Seen from the point of view of the fence as it's being riddled with bullets, Spock has his arms folded across his chest. However, in the closeup shot of him and Kirk, just before Kirk reaches for his pistol, his arms are at rest.
Just after 3:33 and when Spock says to Captain Kirk "I prefer to be a welcome guest", Kirk turns back to his seat and a fart is heard.
When the Earps and Doc Holliday open fire on the landing party, they don't act shocked that the bullets didn't kill them. (However, Virgil momentarily glances down at his pistol and back up at them. He seems to be the only one to show confusion.)
When Wyatt takes on Kirk single handed and gets beaten, neither his brothers nor Doc Holliday intervene. They don't even watch them fight, they remain standing and staring straight ahead at the remaining landing party members.
Spock prides himself on his knowledge of the Old West. However, he apparently forgot that Billy Claiborne was not the only survivor of the famous gunfight. Ike Clanton survived as well.
Early in the show when Captain Kirk is communicating with the alien he refers to the "Spaceship Enterprise" rather than Starship Enterprise.