Tomorrow is Yesterday - S1-E20
Question: When Christopher is beamed back into his fighter jet, he doesn't see the Enterprise in the sky any more. The slingshot effect returned him to the instant before first viewing the Enterprise. He may not have any physical evidence to report now, but he would still have his "memory" of all the events that happened after he was first beamed aboard. If that's the case, he would now have to remain utterly silent about his adventures so as not to risk any change to the future birth of his son. Right?
The Corbomite Maneuver - S1-E11
Question: In this episode, the navigator, Mr. Bailey, has an earpiece only for the length of time it takes to notify the crew of the message coming in over the navigation beam. Why is it that no time before, or since, that anyone at the conn or navigation positions never had one?
Question: Why do the ship's weapons and hand weapons have different colour effects?
Answer: It most likely represents varying power levels. Think of fire; as its temperature rises, its color changes. Energy weapons are likely similar.
For the World is Hollow and I Have Touched the Sky - S3-E8
Question: How did Dr McCoy know that Kirk and Spock were going to beam down? Kirk didn't call him to beam down with them.
Answer: Their mission is to explore strange new worlds, seek out new life and civilizations. He knew they wouldn't just fly away. Besides any expedition would require a leader, a scientist and a medical doctor.
Question: If McCoy was so worried about Kirk, why he didn't stay on the planet to continue the search?
Answer: McCoy's place is aboard the Enterprise. If they fail to deflect the asteroid, everyone left on the planet, including McCoy if he remains behind, will be killed. If they are successful, then both Spock and McCoy can return to continue searching for Kirk. McCoy, being a Star Fleet officer and a doctor, knows that his first duty is to the Enterprise and its crew. "The needs of the many outweighs the needs of the few, or the one," certainly applies here, and it is what Kirk would have expected of him.
Question: How did Dr. McCoy know that the figure next to Kirk and Spock was Surak? The Enterprise was not watching when they were introduced.
Answer: Everyone knows who George Washington is, also Abraham Lincoln, Thomas Jefferson and countless others. When you join Starfleet, you have to know other planets, their people and their histories.
Question: Surak is a Vulcan with better hearing than humans and greater strength than humans. How was he able to be killed so easy?
Answer: Maybe not so easily, Klingons are known for their strength and fierce fighting styles, plus he went up against four of them.
Question: When Gary Seven received the three ID cards from the computer, one ID is for the police homicide department. However, this ID card is not used. What was the reason for issuing it?
Answer: It's not explained. However, Gary Seven was originally supposed to be a character in a separate TV show. A pilot was filmed, but the show never materialized. Footage from the pilot was later incorporated into the Star Trek episode, "Assignment Earth." Presumably, some of the footage that was used didn't fully relate to or explain the revised plot, creating inconsistencies. Also, at the end, Spock tells Seven that he and his new team have, "many interesting experiences ahead of them." That could indicate the unused I.D. was intended for a future purpose.
Question: Spock says Kirk went to a time ahead of him and Dr. McCoy. How did he know that?
Answer: Spock understood how the machine worked, by sending a person to the time they were viewing. When the three were near the time portal, they could hear each other and those around them. Spock would have been able to hear the group of people who took Kirk and heard them talk about thievery, purse cutting, and the law, etc. He made a logical assumption Kirk is in a more advanced and "civilized" time period that would have to be much later than the ice age.
Question: There is a part after Charlie's examination where he's walking down the hall, and finds a man lowering a pole down into a vent of some sort. What exactly was that guy doing? (00:06:06)
Answer: It's never really specified, but the poles were most likely a way of going from deck to deck for engineering crew.
Answer: He beamed back into himself, He jumped into a point in time before he was on the Enterprise. So When he didn't see the starship he had no memory because he never left.