When Riker is carrying Palmer away from the native's building, he is halfway up the hill. When the camera shifts to those pursuing him, and then back to Riker, he's still only halfway up the hill.
When Picard and Riker speak with Dr. Barron aboard the Enterprise, the stars outside move in the close shots, but are stationary in the wide shots.
When Oji's father wakes up on the Enterprise, there is no logical reasoning for him to realize that Picard was the captain's name as opposed to a commonly used word. Since he would not have had the language universally translated, unless the crew forgot to disable it, everything should have sounded gibberish.
The weapon is a compound bow, one that has wheels or cams to increase power. Some might suggest that this would be inconsistent with the presumed stage of development of this culture. As these people are "proto-Vulcans" and, as seen by Oji's sextant, more prone to scientific discovery, there is no reason to doubt that they would apply the knowledge of a pulley to the development of a hunting bow.
Riker and Troi get surgically altered to look like the native people. Mintakan men have no facial hair. If Riker wanted to blend in, he should have shaved or sent down someone else who was clean shaven. Not a single person he met wondered what that thing was on his chin.
When the Mintakans are following Troi, Oji turns back because she says the sun is near zenith and she needs to take her astrometric measurements. Zenith means the point overhead, yet the shadows indicate that it is late afternoon.
However, long shadows only mean that the sun is low in the sky. (On Earth, there are long shadows at noon, in the winter.) In the absence of other information, it is impossible to know what time of day it is from the length of shadows.
It is unlikely there there would be birds with exactly the same calls as here on Earth. However, they may just sound similar and, perhaps, there are only so many varieties of possible sound from the syrinxes of bird-like creatures.
When Picard and Nuri are in the observation lounge, the panels surrounding the windows, which are intended to imply a thickness of window material, are coming off the frame. One shows curling and a number have clearly separated from the structure.
At one point aboard the Enterprise, a scale model of the ship is shown, but with call letters NCC-7100. If the model was supposed to represent the actual Enterprise, then someone got it wrong, as the call letters of the ship were NCC-1701-D.
The arrow in Liko's bow when he aims at Troi, and then shoots at Picard, has a blunt tip. This is not the type of arrow to use when attempting to kill any animal the size of a human. It would hurt, but it is doubtful that it would penetrate.
From the observation lounge, the Enterprise appears to be orbiting the planet backwards when compared to the exterior scenes.
When the archers are chasing after Riker and Palmer one of the archers can clearly be seen loading a compound bow. Clearly not Bronze Age level technology.
Although the costuming of the characters on Mintaka is not out of place for the Bronze Age, that would be based on Earth history. There would be no reason to expect the civilization on a foreign planet to clothe themselves in the exact same manner.
When Captain Picard tells Data to beam Nuria 'directly' to transporter room 1, there appears to be no logical reasoning for it. Firstly, through the whole 7 seasons, even though bridge staff operate transporters throughout, at no point before or since was it specified that they should be beamed 'directly' to the transporter room. This occasion is no more or less routine than those other times, so there is no need to specify it. Secondly, after this, he goes to the transporter room and operates the transporter himself from there, thus there is still no logic to his request to Data just moments earlier.
Riker and Troi forget that the best way to lie is to tell the truth--just not all of it. When the Mintakans are speculating about why "the Palmer" was cast out by "the Picard", one of them could have suggested that "the Picard" sent "the Palmer" to Mintaka to accomplish a task and now awaits his return, a suggestion that would have been strengthened by the fact that two hunters have just returned after being sent by Nuria to accomplish a task (namely, getting meat).
(at around 30:30) When Picard shows Nuria the view of her planet from the Enterprise, what appears to be a boom mic is visible on the top of the screen.
When Dr. Crusher contacts the Enterprise to beam up the injured Liko, the reply can be clearly heard as, "Yes, Captain" rather than "Yes, Doctor." This error has been corrected in the remastered release.