In the opening scene, a male extra seems to be walking up the ramp to the computer interfaces, then disappears in the next shot. Instead, a female extra in blue appears walking up, while in the next shot she is back on the lower part of the bridge behind Data, appearing to be running fast in circles around the bridge. Laters an older-looking extra in red keeps appearing/jumping through scenes unreasonably.
When Picard finds the display screen for the automated salesman, the editing shows him clearing the dirt off the same screen 3 different times.
When Geordi is talking to the two young officers on the battle bridge, he raises his right hand in a fist in front of his stomach, then lowers it again. When the camera angle changes, his fist is suddenly back up in front of him.
When he decides to beam down to the planet, Picard leaves Geordi La Forge in command of the bridge. Geordi is a lieutenant junior grade. Troi is a fully commissioned officer with a rank of lieutenant commander, a full two ranks above Geordi. It might seem to make no sense to leave a junior officer in command while a senior officer is present on the bridge, however, as Troi is not a command officer, it would actually be improper to put her in charge.
Geordi says he is nervous about taking the Enterprise into battle because there's a good chance it will be "blasted out of the sky." The term "sky", as used literally, would only apply if he planned on taking the ship into the planet's atmosphere, which there is no indication he ever considered. However, he is more likely to be using the term more broadly, since the sky is everything above the planet, not just within the atmosphere.
Yar fires at the probe, destroying it and Riker's force field. However, the leaves and branches between her and the probe are unaffected.
Data states that the drop into the cavern is 11.75 meters. The actual set shows a drop of roughly half that distance. Either the set was not able to be constructed to match the dialogue, or the American writers in the 1980s did not have a firm grasp on the metric system.
(at around 21 mins) Data throws Tasha out of the way of the probe's weapon wire, then jumps after her. It's an obvious stunt double for Data.
The targeting schematic in the cave shows the two remaining targets (Riker and Yar) moving very quickly away from the cavern. When the scenes switches to Riker and Yar, they are very slowly strolling.
When Data frees Riker from the stasis field, Brent Spiner can be seen smiling a little as the characters run away. Data should not be able to smile on instinct like a human as he has no emotions.
When Picard tells the peddler that he's interested in buying the weapon, it shuts down and the ground weapon vanishes. However, the space weapon not only remains, but continues to be a threat, despite the 'demonstration' having ended.
The targeting probes are meant to be part of the ultimate weapons system, capable of adapting to and destroying any enemy, yet, apart from the one that puts Riker into a stasis field, none of them ever hit a single target.
Lt. Logan chastises La Forge for staying in orbit of the planet, then, as soon as La Forge gives the order to leave orbit, Logan chastises him for leaving the away team behind. The away team would have been left behind had La Forge taken Logan's original suggestion.
Data says that in order to attempt to free Riker, he will need to know the exact frequency of the force field holding him. He'd already been scanning the force field for some time. Surely those scans would have told him something as simple as the field's frequency. Indeed, he then draws his phaser and begins the process of freeing Riker without conducting any further scans.
The Enterprise is scanned for language, but then a probe later has to generate a hologram to personally ask for the ship's specifications.
Immediately after the orbital weapons probe is destroyed, Geordi orders shields dropped so they can beam the away team back. The ship would still be skimming the planet's atmosphere and thus dropping the shields would cause significant damage.
When Geordi informs the away team that there is an energy reading near them (another probe, as it turns out), the away team responds by all looking in the same direction, allowing the probe to approach from behind. Surely a well-trained team of military/exploration officers would look in more than one direction for an imminent threat.
After Data frees Riker from the stasis field, Yar says "The Captain and Doctor Crusher can't be far away". As far as Riker knew, Picard was still aboard the ship, and since one of his duties is to keep the commanding officer from risking himself unnecessarily, it seems odd that he doesn't even question what Picard is doing on the planet.
Geordi orders the Enterprise to warp 5 for 28 seconds, then a full stop, after which the saucer section will detach from the stardrive section. He orders Logan to take the saucer to the nearest starbase while he commands the stardrive section to return to the planet to rescue the away team. The saucer section is incapable of warp speed on its own, as the warp core and engines are location in the stardrive section. Taking the saucer to a starbase under impulse power could take weeks, months, possible even years. However, the saucer section is capable of sustaining a warp field and "coasting" at faster-than-light speeds, if the ship it detaches from is moving at warp speed when it separates. It would have been a better plan for Geordi to have detached the saucer while at warp to give it a better chance of making to to the starbase in a timely manner.
When Dr Crusher is injured, Captain Picard tends to her injury. Only later, when she believes she has lost a lot of blood, does she tell the Captain of her leg injury.