Riker, Geordi and Data are in different positions when the Ferengi bring an unconscious Worf to their location.
When speaking with Portal, the positions of the members of the Enterprise away team and Ferengi vary wildly between shots.
When Riker reawakens and begins threatening the Ferengi, he is squatting with both knees in front of him and his elbows resting on his legs, with his hands dangling freely. In the reverse shot, he is positioned with his right knee forward and his left knee down on the ground, with his arms down by his sides and his hands bracing against the ground, helping him balance.
The crew gather together as life support fails and the ship loses heat; however, they are shown gathering in a compartment with windows and a sloped ceiling, indicating that these rooms are adjacent to the outside hull of the ship. These would be the rooms to avoid in this type of emergency. You would want to gather together as close as possible to the center of the ship, or as far as possible from the outside hull.
At around 25:00, Picard ends communication with Tarr. The cut-off signal is heard, followed by Tasha announcing that hailing frequencies are off, but Tarr's face remains onscreen as if watching them. If "frequencies" only referred to the Enterprise's hailing frequencies turning off with the Ferengi lines still broadcasting, then that would mean Tarr looked at his own blank screen quizzically for four seconds before finally cutting out.
Deanna states that she senses Tarr, in his initial communication, was hiding something. It is later established that Betazoids cannot read Ferengi minds. However it is not explicitly stated that her Betazoid powers are the basis of her conclusion. Being a ship's councilor, Troi would be well-versed in body language and adept at detecting verbal indications of deception.
During the initial tactical briefing in the conference room, Data gets his fingers stuck in a Chinese finger trap. Picard is irritated but Geordi laughs, "My Hero," and Picard assists Data out of the trap. During the subsequent close-up shot of Data's fingers, the tips of his two fingers that were stuck in the trap are clearly flesh tone, pink, as the make-up has clearly been removed by the inside of the finger trap.
Data's display bar shows both Klingon and Federation information, upside-down.
When Doctor Crusher says that they "...won't have to worry past 70 below...", Picard replies that "It feels like that now." One would expect that if it feels that cold, their breath would be visible.
Portal swings his staff while approaching Riker showing off his speed and dexterity. It's obvious that the video is at double speed for this effect.
Early in the episode, while on the bridge, Picard orders Geordi to go to Engineering. As Geordi walks toward the turbolift, the doors open for him prematurely.
When they spot Geordi on the alien planet, Riker and Data run towards his location. They start from the same point at the same time, yet Riker arrives at Geordi's location well before Data. Given Data's physical superiority to humans, he should have arrived first.
Picard gives Riker permission to beam a box of Chinese finger puzzles to the Ferengi ship, but no order was given before the Enterprise left orbit.
Children playing in the conference room (a restricted area) upset Commander Riker and Captain Picard, yet there's no way children should be able to access any restricted area. The ship's computer controls all doors. How were the children able to override the ship's computer?
The crystalline structures are absorbing energy from the Starfleet officers' phasers and the Ferengi energy whips, also rendering their communicators and tricorders inoperative. It is said to be a similar effect to what is happening to the starships in orbit, which are being drained of all power. Yet Data, an android who runs on power cells, is unaffected, as is Geordi's VISOR. Geordi even uses his VISOR's enhanced sensing capabilities to help deduce what is going on. Logically, neither Data nor Geordi's VISOR should be functioning, and since the Enterprise crew was aware, at least to a degree, of what was occurring on the planet's surface, including the two of them in the away team comes across as reckless.
Despite possessing great strength and superior intelligence, Data could not free himself from a simple Chinese finger puzzle.
At one point it is said that the Enterprise will only be able to maintain its shields for another 63 seconds. Several scenes later (taking at least 5-10 minutes, though more time may have elapsed during the scene transitions), Yar tells Picard she will have to shut down shields to divert their power to life support. The shields should have long since powered down by then.
The premise of this episode is that the Enterprise crew attempts to recover a piece of stolen equipment. Replicators would make such a recovery pointless. The equipment is not rare or valuable. It would be far easier to simply replicate a replacement. Due to the risks of damage to the ship, of losing crew members, and of starting a war, the recovery of the equipment is not justifiable.
Geordi makes the comment "point 300 milliseconds," which is nonsensical. it's either .3 seconds or 300 milliseconds or .3 milliseconds - not what he stated.
While dealing with Portal 63, Data says, "I'm afraid not," breaking his rule of never speaking in contractions.
On the planet, the transporter beam-down separates the landing party. Riker tries to find the others by shouting for them above the thunderstorm, never by his communicator. After finding Data and Geordi, Data states that communication is "gone," but Riker should have already known this by the habit of always checking his combadge.
The Ferengi repeatedly refer to the Enterprise's away team as human. Of the 5 members of the away team, only 3 are human. Worf is a Klingon and Data is an android.
The Ferengi try to convince Portal that the humans are not to be trusted because they adorn themselves in gold - a wasteful use of a precious metal - but a running gag on Star Trek: Deep Space Nine (1993) establishes that the Ferengi do not assign any value to gold. The only use they have for gold is to mix it with latinum to produce bars of gold-pressed latinum, which they use as legal tender.