Though Lt. Cmdr. Remmick states that it is nighttime ('a quiet night'), the exterior shots of Starfleet Headquarters shown both before and after this line, but still within that same evening, show it to be daytime.
After we see Riker crash through the glass table and become unconscious, the next camera angle shows his head and left arm are in different positions.
From the time Worf puts Riker's still unconscious body down so he can fight the admiral, to when Dr. Crusher stuns the admiral and goes to help Riker, Riker's head and right hand have changed positions.
About 24 minutes in, you can clearly see that Lt. Cmdr. Remmick has three full pips, indicating the rank of Commander. However, near the conclusion, he is back to two and a half pips, indicating his correct rank of Lt. Cmdr.
When Picard and Riker are with the admirals on earth, both of them including Capt Scott, clearly had their heads turned to the camera at times and there are no protrusions visible.
When Riker orders La Forge, at the helm, to increase speed from Warp 5 to Warp 6, La Forge replies, "Aye, Sir, full impulse." Full impulse speed, is slower than even Warp 1.
After the guests eating the dinner of worms are subdued, Picard and Riker run after Admiral Aaron. Picard hollers "Aaron!", to which Aaron then turns around, and fires a phaser at the two. In the process, Picard is able to dodge the beam after the weapon is fired, which would be impossible to do being light travels at 186,000 miles per second.
When the Admiral beams aboard the Enterprise with the life form, he and Cpt. Picard are talking in the hallway and a male crew member is in the background wearing a what looks like a female's uniform. There are no "male" or "female" uniforms in Star Trek: The Next Generation. Both men and women can wear pants or skirts, whichever they choose. Male crew members wear skirts on several occasions in Season 1.
When Data reviews all Starfleet decisions for the past six months, a camera angle shows all the information on his screen, including the image of what seems to be a parrot. The involvement of a parrot with Starfleet Command decisions may seem unlikely, yet it is not impossible. One example could be that this image is the symbol of an alien world or alliance Starfleet has dealings with. Or it could be an actual alien bird that has been recently discovered and needs further studying. In each case, its connection with command decisions would become plausible. A similar image was seen in The Naked Now (1987): during the scan of the records, we quickly see a parrot with a barely distinguishable human head (Gene Roddenberry's) on a perch wearing a Starfleet uniform, complete with insignia. This is a reference to Gene's fan inspired nickname, "The Great Bird Of The Galaxy."
When Geordie is thrown against the door by Quinn, the door just flies apart. Besides the fact that it is unlikely that doors on the starship would just fall apart so easily, they also have no bearing in the surrounding wall, making it obvious they are props.
The face of Admiral Quinn's stunt double is occasionally seen during his fights with both Riker and Worf.
When Picard and Riker are chasing Admiral Aaron, the Admiral fires at them, striking the wall, and painting, behind them. There is no visible damage to the wall or the painting afterwards.
Beverly stuns Admiral Quinn with her phaser with three phaser blasts. If you look carefully, she doesn't have her thumb pressed on the trigger for the final blast, yet a beam still manages to come out of it. Further, after the last blast, she is seen pressing down on the trigger, and no beam comes out at all.
As Worf is thrown against the wall in the Admiral's quarters, the replicator shakes for a moment revealing the fact that it's a prop.
When the fight with the admiral first starts, and Riker see's what he's up against, he calls for emergency help on his communicator, but it takes a long time for Worf and La Forge to show up. When they do, Riker is unconscious, but when the admiral says that he slipped, they don't question that it was Riker's voice that called for help.
When Riker announces an emergency and calls for help from the admiral's quarters, Geordi and Worf arrive quickly but unarmed. While it makes sense that Geordi would be unarmed, Worf is head of security and is shown later in the series to be carrying a phaser at all times, even when at his tactical post on the bridge. Worf should not be unarmed when responding to an emergency called by the acting captain of the ship.
Similary, why is Dr. Crusher the only crew member who arrives with a phaser drawn, ready to shoot? Shouldn't a security team have followed up?
Similary, why is Dr. Crusher the only crew member who arrives with a phaser drawn, ready to shoot? Shouldn't a security team have followed up?
When Admiral Quinn beams aboard the Enterprise, he has a case containing an unknown alien creature that he sneaks aboard. The transporter's bio-filters should have sounded an alert.
Captain Walker believes that his first officer and chief medical officer have been compromised by the growing conspiracy within Starfleet. It is later revealed that anyone infected by the alien creatures has a visible tendril sticking out of the back of their neck. Surely Walker's officers wouldn't be able to hide such an obvious physical abnormality from their paranoid captain.
Riker calls for emergency security to the admiral's quarters. The only two people to respond are Worf and Geordi, who were stationed on the bridge, and Geordi's not even a security officer. Surely there must have been security personnel stationed closer to the guest quarters.
(at around 12 mins) Cmdr. Riker issues the command to La Forge to increase to Warp 6, to which La Forge replies "Aye sir, Full Impulse." Full Impulse Drive on the Enterprise-D is equivalent to 1/4 the speed of light, while Warp 6 is roughly equivalent to somewhere between 100-200 times the speed of light (depending on warp scale used).
On the mining planet, Captain Keel tells Picard about the conspiracy and to tell no one about their meeting. Then, before Picard leaves, Keel tells him to say hi to Beverly (Crusher) for Keel.
After suspecting that Admiral Quinn is not himself, Picard pulls Riker into the transporter room for a private conversation, in front of a low-ranking transporter technician. The technician is not seen, but Picard acknowledges their presence after the conversation ends by stepping onto the transporter pad, looking in the direction of the console, and telling them to "energize." If Picard wants to keep his suspicions and reasoning limited to himself and the senior bridge staff, openly discussing sensitive information is not the way to do it.
Picard seems impressed that the admirals "keep up with [the Enterprise's] duty roster" after they mention Commander Riker by name. Riker is the executive officer of the fleet's flagship and was assigned there nearly a year prior. Knowing the name of its well-ensconced second in command is hardly "keeping up with our duty roster."
Captain Walker tells Picard that their meeting never took place, then almost immediately tells Picard to say "Hi" to Beverly for him.