In the cargo bay where Lutan arrives, a roll of carpet is laid down for him to walk on. However in the next scene the roll has been turned around for Lutan's second to unroll it by kicking it.
In 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.
During Troi's conversation with Picard and Yar, where she recommends that Yar accept Yareena's challenge, her arms change between hanging beside her body and crossed behind her back.
When Geordi is shaving, the razor is on his right cheek when viewed from over his shoulder, but when the camera angle changes to a front view, the razor is on his left cheek. It is again on his left cheek when the camera angle changes.
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.
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.
When Yar is kidnapped, the crew wonders what to do. Picard dramatically orders a barrage of torpedoes as a show of force but Yar's location could have been determined via her combadge, 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 feasible.
In the holodeck training, Yar says that her holographic opponent won't move until her actions activate it, yet the actor portraying the holographic fighter can be seen wobbling slightly the entire time he is supposed to be unmoving.
It's apparent Yar meant the fighter would not make an active move; martial artists, even in video games, move slightly so as to not be caught "flat-footed".
During the fight between Tasha and Yareena, from one angle it is clearly Tasha's stunt double fighting. (This is necessary, as seen in other episodes, because the actress clearly had no martial arts skills.)
The Ligonian delegation arrives in the Enterprise cargo bay carrying a carpet, which is then rolled out. It is exactly the right length to reach from where their leader transported in to where Captain Picard was standing. There is no way that they could have known the exact length of carpet they would need.
When Doctor Crusher is attending to Yareena in the transporter room, the doctor is seen to be wearing a wristwatch.
When Picard, Riker, and Troi are leaving the bridge, Picard tells Data "You have the helm, Mr. Data" a studio light can be seen reflecting on a panel near the turbo lift.
Studio lights and set rigging can be seen reflected in the conference room windows.
At the end, if the plague in Styris IV is so bad, why do they go there at warp 3?
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.
It is never explained how the Ligonians could have a vaccine for a virus they have never encountered. Ignoring the unusual idea that a less developed culture could have a singular medical development that eludes all of the Federation, vaccines are made utilizing a weakened form of a specific pathogen. If the Ligonians never encountered that pathogen, they'd have no material from which to develop a vaccine.
Data makes Geordi laugh by accidentally mirroring the language of the joke he'd just told (which Geordi did not find funny). He states that the gaffe was unintentional, and his tongue merely slipped. Data is supposed to be far too efficient and precise to make such an unintended verbal slip, and indeed never does so again.
After telling Geordi a joke, Data says "...includuling the kiddlies, I've told 662 jokes...". But Data is unable to use contractions such as "I've" so he should not have been able to say this. He uses several other contractions in the same episode.
When Picard presents a ceramic horse figure as a gift to Lutan, he incorrectly states the gift is a Chinese Song Dynasty 14th century figure. (Data corrects him saying that Song Dynasty was 13th century.) This horse figure is actually a San Cai (three color) ceramic, and these were produced in the Tang Dynasty (7th-10th centuries).
In the holodeck scene, Tasha Yar ties an incorrect knot with the belt of her Aikido gi. Both ends should hang down and the knot should be symmetrical from top to bottom.
When Picard leaves the bridge to receive the Ligonians, he tells Data, "You have the helm." Since Data is already at the helm, the order is redundant. If he wanted Data to take command while he is away, the order should be, "You have the bridge."
When Picard leaves the bridge to go to Cargo Bay 1 to meet the Ligonians, he tells Data that he has the helm, when in fact Data is sitting at OPS, not the CONN which is the helm.