The calendar in the background at the mission (when Edith Keeler talks to Kirk about a place to stay) shows a 30-day month, with Wednesday the 14th in red, indicating a holiday. However, none of the 30-day months in 1930 started on a Thursday, and the only month in the United States with an observance that is always on the 14th is June (Flag Day). In 1967 (this episode was filmed in February of that year), Flag Day fell on a Wednesday, therefore it is likely that this is a 1967 calendar.
Spock picks a combination lock to obtain tools. This type of single-dial combination padlock was first marketed by Master Lock in 1935, five years after the events of the episode, and the early models had a metal dial, with the plastic dial depicted on the show coming at least two decades later. The particular lock Spock picks appears to be a much later copy of the Master design, possibly from the late 1950s, but much more likely to be from the early to mid 1960s, which was when the show was filmed.
When Kirk is talking to Edith on the stairs, Edith stumbles and Kirk catches her. Before and after she stumbles, Edith is wearing two shoes. After she kisses Kirk and walks back up the stairs, her right shoe is missing.
Despite having a security alert aboard Enterprise to find Dr. McCoy--which everyone on duty at least would be aware of, Transporter Chief McCoy does not turn to face McCoy when he enters the transporter room and the sound of the doors opening is heard.
The Guardian of Forever first speaks in response to Kirk's questioning of its origin by saying "Then what is it?" by responding "A question." Moments earlier, Kirk had asked the same question in slightly different wording, "What is this thing Mr. Spock?" with no response, though this question was directed to Mr. Spock.
When Kirk walks Edith home he tells her about a novel that will be written by someone from another planet, circling the far left star in Orion's Belt constellation which he points to. However, when the shot changes to the sky, it is overcast at dusk and no stars can be seen.
McCoy sneaks up to and knocks out Transporter Chief Kyle with two well placed Karate chops to the small of the back and the neck area. When Kyle recovers he is seen being helped to his feet by one of the security men. He immediately tells Capt Kirk over the intercom two things that Dr. McCoy had beamed down to the surface. Having not seen McCoy he could not have known for sure it was him (though it would have been a good guess).
When Uhura and one of the security men are looking for Dr. McCoy on the planet they walk by a large rock that he is hiding behind. As they walk past the rock on their right, they are looking only ahead and to the left, but never to the right. Had they looked to the right they would have seen him squatting behind the rock. Not the normal "good work" you would expect from Uhura and a security man.
When McCoy jumps through the portal, Capt Kirk is next seen finishing a dive to try to tackle him. However, he was 2-3 seconds late. He ended up 3 feet away from the portal with Spock between him and the portal. He probably would not have dived after nothing.
When Kirk and Spock are running from the police, you can tell that they simply run around the block back to the exact same alley. The two barrels, one rusty and one yellow, are still in the exact same spot.
When McCoy arrives in 1930 NY, he believes he is in a fabricated environment and marvels at the detail of reconstruction. As he leans on a column less than 6 inches in diameter he remarks on the detail, "...even down to the cement columns." implying the free-standing column he is leaning on is made of cement. Clearly, the size and texture of the column would make it metal. A free-standing street column also would suggest a utility pole, none of which would be made of cement.
During the early bridge scene, shots filmed from the front of the bridge clearly show a red uniformed female standing next to the center seat. When the shot switches to the view from the rear, she disappears, even though that section of the bridge is still in shot, and reappears when the view returns to the view from the front. In addition, Kirk looks different in the rear view shot, as if this section was filmed with a stand in for William Shatner.
When McCoy first runs into the area of the portal and away from the landing party, he puts his hand on a brown metal or concrete beam lying flat on the ground (in ruins). However, the beam can be seen moving back and forth with his light touch-obviously a prop.
The goof items below may give away important plot points.
In a scene often deleted for syndication, a bum called Rodent steals McCoy's phaser and accidentally kills himself with it. In the wide shots you can see that the actor playing Rodent is missing part of the ring finger on his right hand, but the ring finger in the close up of the phaser being activated is undamaged.
While seven people beam up and the transporter platform has only six pads, there are several transporter stations on the Enterprise and the extra crewman could have easily been sent to a second platform.