During the phaser fight in the holoship, A Son'a soldier is shot and rolls off the roof of the hut, and when Picard ends the simulation, the soldier is not lying on the floor stunned when we see the full holodeck revealed, unless he was a hologram too.
When Picard is beamed on to the collector ship before facing Ru'afo, he is beamed from another Son'a ship, but he materializes with a Federation transporter effect, not a Son'a one.
When Data opens the door to the cloaked holoship, he and Picard and Anij are kneeling on a raft -note the paddle in Picard's hand. To enter the holoship they need take only 3 steps up (about 3 or 4 feet). But about one minute later, when they come under fire and Picard pushes Anij back out the door through which they came, the surface of the lake is at least 15 feet below the doorway.
When he discovers the holoship hidden in the lake, Data opens a dam and lowers the water level. But when he boards the raft with Picard and Anij, the pier is still at the correct height for the normal water level.
When Data and Picard beam back up to the Enterprise after jumping into the Ba'ku lake, Data's uniform is dry while Picard's is still soaked.
When the crew meets Picard in the Captain's Yacht, the captain tells Geordi and Riker to take the ship and transmit a message to the Federation. If you look at Geordi's collar you see a gold and two black pips (rank insignia). He should have two gold and one black pip for his rank of Lt. Commander (one gold and two black pips does not belong to any rank in Star Trek).
When a bomb explodes at one end of the bridge, several people are catapulted over the parapet in a direction at right angles to the blast.
The second time the crew go to the planet, they faced a surprise attack to which they reply with their phasers while, the first time they went, they were told that no arms were permitted in this society.
Picard sings "heart" instead of "foot" in the second chorus of "A British Tar", despite having the lyrics displayed in front of him on his computer. Considering the stress he's under, he does an excellent job.
While singing "A British Tar", Data, who supposedly has perfect recall, sings the wrong notes for part of the song. Then again, Data was "malfunctioning" during this part of the movie, so who knows what effect this could have on his perfect recall.
Data used a contraction in the scene where the cave collapses, saying "it's safer over there." Although the series established in later seasons that Data can not use contractions, he had the emotion chip installed into his positronic net in Star Trek: Generations (1994) which would likely allow him to not only experience emotions, but to use contractions as well. Episodes in early seasons of Star Trek: The Next Generation (1987) showed Data using contractions. Also worth mentioning that although Geordi tells Capt. Picard that he didn't take his emotion chip with him, it is possible he reinstalled it during the course of the movie.
The effect of the planet's rings caused Geordi LaForge's eyes to grow back. In the season 2 episode "Samaritan Snare" it is established that Capt. Picard has an artificial heart. The metaphasic radiation would have caused him to re-grow his own heart. Additionally, in the fifth season episode "Ethics", Worf suffers a catastrophic spinal injury. An experimental medical procedure generates a new spine. His own spine would grow back due to the metaphasic radiation. In actual fact, the radiation causes Geordie's optic nerve to regenerate, not for him to actually grow new eyes. It does not actually grow new organs, it simply regenerates and reactivates damaged cells to a certain degree, so Picard would not have miraculously grown a new heart and Worf would not have grown a new spine (though Worf's implanted spine was grown by cloning his cells anyway).
As with many other depictions of humanoid aliens, most of the female aliens wear dresses/skirts, all the male aliens wear pants. Clothing style of this sort would not be a universal development across all of the humanoids, yet Star Trek, when presenting alien humanoids, always adheres to this style of clothing. However, since nobody knows what alien men and women would wear, the producers of Star Trek are free to depict them in any way they like.
In the beginning, when Data is being chased into the village, the stone bridge shakes and flexes like a wooden prop as the children run across it.
During Riker's bath tub face shaving scene, it is obvious that his face has already been totally shaven.
When Picard shoots the Son'a guard on the holoship, a crash mat can be seen when he falls off the roof.
Before the Ru'afo and crew are transported to the Holodeck, Data mounts an attack on the Son'a ship whilst communicating with Picard. Picard, who is on the Son'a ship, crawling through a tube, out of uniform with no communicator is able to hear and speak to Data. Just prior to this scene Picard asks Gal'na if he can get him to a transmitter so he can speak to Data and Worf, emphasizing the fact he is unable to communicate with his crew.
When Picard is first meeting with the Baku, there are children playing a hacky-sack type game in the background. During two short shots, the children can be seen making kicking motions but there are no hacky-sacks to be seen.
While Picard, Riker, Troi, and Crusher are on their way to the reception, Picard is paged by an ensign on the bridge with a message saying Starfleet was requesting an ETA to the Goren system. Riker tells Picard that there's a territorial dispute there, Picard never answers the ensign back and simply proceeds to the reception.
The Ba'ku philosophy has rejected the use of weapons and violence. Yet they have no apparent problem in letting others use violence for them.
When Ru'afo socks Dougherty in the face, he obviously misses, yet we hear a punch effect.
After Picard rescues Anij from the water, Data says, "In the event of an emergency, my body can be used as a flotation device." Data then "rises" above the water as if he is inflating. The platform that raises Brent Spiner higher in the water is visible through the water underneath him.
Shadow of equipment visible on the cave wall, just before Picard goes through the hole he has blasted in the wall.
In the beginning of the movie, after Picard, Riker, Troi, and Crusher enter the turbolift, the turbolift doors close and the reflection of the camera can be seen in the shiny turbolift door label.
Admiral Dougherty tells Picard - admittedly, perhaps deliberately - it could take ten years for the Son'a to start feeling the effects from the metaphasic radiation; yet the entire Enterprise crew, newly introduced to them, begin to feel effects almost immediately upon entering the planetary system (i.e. Geordi's eyes). Picard doesn't contradict this statement by noting the example of his crew's reaction to the radiation in arguing more strenuously against the Son'a plan, which would make unnecessary the subsequent actions of him and the Enterprise crew.
Riker starts getting frisky, LaForge starts rejecting his optical implants and gains the use of his natural eyesight and Worf begins going through Jak'tahla (Klingon puberty), yet the Enterprise has been there for less than 12 hours and neither of them has been on the planet at the time to have been exposed to the regenerative metaphasic radiation like those who have spent any time on the surface.
During the battle with the Klingons, Picard orders Worf to prepare a "full spread of quantum torpedoes." But in the very next scene, Worf fires just a single torpedo.
Troi comments that she had never kissed Riker with a beard
before. Yet Troi had kissed the bearded Riker in Ménage à Troi (1990), as well as in several other occasions on Star Trek: The Next Generation (1987).
While at the lake, Data says that he was designed as a flotation device. This is not true. In Descent, Part II (1993) Geordi reminisces about when he and Data went sailing on Devala Lake. Data decided to go swimming, jumped out of the boat and sank straight to the bottom. Because of his lack of buoyancy Data was forced to walk 1.46 kilometers along the bottom of the lake to get back to the surface. Even if he has altered his body to accomplish this task, he was not "designed" that way by Soong.
At 22:54, when Picard first meets the Baku, He first introduces Doctor Crusher & then Counselor Troi, Counselor Troi nods first & then Doctor Crusher, as that is the order they are standing. Patrick Stewart says the names out of sequence and Marina Sirtis & Gates McFadden end up responding to the wrong character names.
When the Admiral goes to talk to Capt Picard, there is a kidnapped Ba'ku woman smiling and laughing with another unseen actor, when seen again, she appears as a victim again.
When Picard is planning to beam down to aid the Baku, he prepares to bring a small arsenal of weapons with him. He must know none of the Baku would be willing to even pick up a weapon let alone fire it.