The City on the Edge of Forever - S1-E29
Factual error: This episode takes place in NYC during the 1930's, but after McCoy's phaser is stolen in the exterior shot of the buildings a fallout shelter sign can be seen. These signs were put up no earlier than 1961.
The City on the Edge of Forever - S1-E29
Factual error: Edith Keeler says to McCoy, "My young man is taking me to see a Clark Gable movie." In 1930, Clark Gable was an uncredited bit player who had last made a film in 1926 - Edith, a New York charity worker, would not even have encountered his name.
The City on the Edge of Forever - S1-E29
Factual error: The song "Goodnight Sweetheart" was written and first performed in 1931. This episode takes place in 1930, one year before.
The City on the Edge of Forever - S1-E29
Factual error: Spock picks a lock during the great depression, but the lock is from the late 50's.
The City on the Edge of Forever - S1-E29
Factual error: When Edith Keeler is killed by the truck, it is traveling at about 25 miles per hour. At that speed and her weight around 120 pounds, she would have been thrown about 50 feet. However, she's seen dead on the ground in front of the mission where she was hit.
Answer: Kirk was getting his physical and Dr. McCoy probably turned off communications, because if he hadn't, Kirk would have left and headed straight for the bridge, leaving McCoy irritated.