Question: When Kirk and McCoy try to rescue Chekov at Mercy Hospital, Kirk removes the 20th Century medical team into an adjacent room and uses his phaser to instantly fuse the metal door lock. The medical team cannot directly see Kirk do this, as they are visibly several feet away on the other side of the door. It's also safe to say that the medical team has never seen a phaser and can't comprehend its function or capabilities. As Kirk turns away from the door to rejoin McCoy, the trapped medical team only then rushes up to the door, and the trauma surgeon exclaims, "He melted the lock!" However, it seems that you'd have to laboriously dismantle the doorknob to determine that the lock's internal components were fused. So, how did a 20th Century surgeon deduce at a glance that Kirk had somehow melted the lock?
Question: Kirk and crew deliberately disclose crucial technological secrets, extend the life of a random stranger, deliver future technology to a primitive military power, abduct a cetacean biologist, and actually contribute to the extinction of a species during their brief stay in 20th Century San Francisco. Specifically: Scotty reveals the secret of Transparent Aluminum 150 years too early; McCoy arbitrarily uses 23rd Century medicine to cure a seriously ill 20th Century woman; and Kirk chooses to remove Gillian from the 20th Century. Perhaps most importantly, Chekov leaves behind a Starfleet Communicator and a Type 2 Phaser in the hands of the U.S. Navy (who would undoubtedly dissect the devices and try to exploit the technology a couple of centuries too soon). Beyond all that, Kirk and crew abduct two breeding humpback whales, one of which is pregnant, and that certainly contributes to humpback extinction in the 21st Century. Given what we think we know about disrupting linear time continuity (many instances are cited in Star Trek canon), how did Kirk and crew return to anything even resembling their own timeline after such blatant and deliberate interference in Earth history?
Question: In the scene where the crew exits the ship via the retractable doorway and gets seen by the garbage men, they had enough power to beam out but decided to walk out regardless, and risk being seen. Yet every other time they beamed in and out of the ship, so why not that particular time? Furthermore, why would the garbage men dismiss it so easily and not report it or return again later.
Question: In a few scenes in the film, the characters mention how people of the 20th century still use money. Key word: still. How is the process of currency different in the 23rd century compared to the present?