The probe object sent by the alien space station is seen flying over the Enterprise in the view screen, but, in the next external shot, it flies under the ship and enters the bottom of the saucer section. In the next shot, from inside the ship the probe is seen passing through a wall when it should be coming through the floor.
When Crusher and Picard leave the room, just after Rivan has been beamed back to the planet, Crusher is ahead of Picard. When the view switches to the corridor outside the room, Picard is suddenly ahead of Crusher.
Rivan's hair while walking through the Enterprise corridor appears different than in all other scenes. In the corridor, her hair has larger, looser curls, with visible dark roots. In all other scenes, including a room aboard the Enterprise, her hair is more tightly curled and colored consistently.
After Picard makes his impassioned plea to the "god" aliens, there is a single shot of Riker saying, "When has justice ever been as simple as a rule book?" In that shot, he is standing alone, with no one on either side of him. In the shots immediately before and after, he is shoulder-to-shoulder with Yar and Worf, awaiting transport.
When the away team first meets Rivan and Liator, Rivan wears a pendant around her neck that is consistently centered. When they start talking about running, Rivan's pendant is suddenly well off-center.
When Worf hears "When in Rome" from Riker, he is confused by the statement. It's later established that Worf was raised on Earth by human parents, so it is unthinkable that he wouldn't have heard of Rome. However, it may be that he is just unfamiliar with the expression, not the city.
When the god-like entity appears through the floor of the bridge, Data's face expresses surprise. Although this may just be him imitating humans, it is unnecessary for an android would do this. However, he commonly adopts human facial expressions, presumably as a deliberately programmed reflex, for the comfort of those with whom he interacts. Surprise is a reaction to the unexpected, not an emotion, so Data's response may be automatic.
While sitting and discussing the "god" aliens' morality with Picard, Data's left eye is very red and a bit of makeup around it has come off.
When Data is meant to be looking at the floating sphere on the bridge, his eye line does not match up with the location of the sphere.
An obvious stunt double is used when Wesley does a series of cartwheels.
An obvious stunt double is used when Data falls on the bridge after the sphere makes contact for the information exchange.
The probe sent by the alien space station enters the bottom of the saucer section. Unless the aliens don't know where the bridge is, the probe should enter the bridge directly.
When the crew first beams down with Wesley Crusher in the background, there is a street light in two different scenes. They are behind Deanna Troi. There also seems to be other poles that do not belong to Rubicun III.
The leg of a light stand can be seen to the left of Picard in the opening bridge scene.
Much of the drama revolves around the Prime Directive, a rule against interfering in the natural development of other cultures. In Trek, the PD mainly applies to making any sort of contact with a society at a low level of technological development. (The threshold is generally accepted to be faster-than-light space travel.) Since the Edo have not yet reached FTL, the Enterprise crew should never have interacted with them at all.
Picard states that the Prime Directive was never intended for a member of any starship crew to lose their life, but it is often stated in TNG that the Prime Directive is more important even than an entire starship crew, that members of Starfleet are prepared to lay down their lives to protect it.
Riker concludes that they have lost contact with the ship after trying his communicator. Without even trying another communicator, he concludes that there is no point and gathers everyone together. Although the audience knows what the problem is, Riker does not. The most likely problem would be a failure of his own communicator. The next logical step would be to have Worf attempt to contact the ship.
When the senior staff return to the bridge after transporting up from Edo, Picard, Riker, Crusher, Worf, and Yar exit the turbo lift. Data, who'd been in command, returns to his usual place at the ops station, which is vacated by an unnamed gold-shirted officer. Strangely, the red-shirted officer at the helm station vacates his seat, which is then taken by Geordi. But Geordi was not part of the crew that beamed up from the planet, nor was he in the turbo lift with them when they returned to the bridge. Geordi was on the Enterprise the whole time and there's no reason for him not to have been at his station.
Riker requesting that Picard beam down to the surface flies in the face of his oft-stated stance that a ship's captain should never risk danger by joining an away team. A more sensible solution would have been, once communication was re-established, to request that the away team be beamed back up to the ship, thus extracting them all from potential danger, rather than requesting that the most important person on the ship join them in their potential peril.
The shadow of the boom mic is visible on the ground to the left of the away team as they take a break from running and young Edo children run by.
Picard directs Geordi to "Get a real look" at the object standing off the bow of the Enterprise. Apparently, La Forge looking out a window with his VISOR can conduct a better scan of the alien ship than all the combined sensors of the most advanced starship in the fleet.
Picard beams down to Rubicun III without a communicator, a violation of common Starfleet precaution.