The substance offered by the Ligonians is alternately referred to as a vaccine and an antidote. A vaccine is something given to someone before they become sick in order to prevent the illness. An antidote is given to someone after a poisonous substance has entered their body to fight it off.
In Star Trek: The Next Generation: Encounter at Farpoint (1987), Picard states that the panel to the right side of his chair is for log entries and intercoms. But when Lutan calls the Enterprise, Picard reaches to the left side of his chair to operate the intercom.
Captain Picard orders a display of photon torpedoes to detonate "1,000 meters short of the planet's surface" (equivalent to 3,280 feet). The torpedoes clearly detonate above the planet's visible atmosphere. While the exact altitude is unknown because of the size of the planet and the atmosphere, the altitude is at least 200-300 km (125 to 185 miles), massively higher than 1,000 meters.
When Yar is kidnapped the crew wonders what to do, and Picard dramatically orders a barrage of torpedoes as a show of force. But Yar's location could have been determined via her communication pin, and she could simply have been beamed back. However, without compromising the Prime Directive (which is what the whole story is all about) and risking a war with the Ligonians, that would probably not have been a viable option.
At the beginning of the fight, it is stated that both combatants will continue until there is a victory and that no one may interrupt. When one of them loses her glove, however, the fight is stopped until the weapon can be returned.
The goof item below may give away important plot points.
In the fight scene, Tasha wears the weapon on her left arm. After defeating Yareena she beams with her to the Enterprise. When we see her in the transporter room the weapon has mysteriously switched to her right arm.