Mr. Worf says that Lt. Hagler is in his quarters on deck 9 section 17. Moments later, Dr. Crusher shows up at Hagler's quarters, the door to which is labeled 09-1947 (presumably section 19). She then asks for a plasma infusion unit to be brought to deck 9, section 19.
Troi, Riker and the rest are in the holodeck trying to remember what's been happening to them; they're asking the computer to recreate a table they all remember being on. When Riker remembers having some type of restraint over his chest, Troi asks the computer to create a restraining arm "attached to the right side of the table at the midpoint." The computer creates a steel restraining arm attached by high steel panels to both sides of the table.
When Riker is in the alien's tertiary subspace universe and is about to pick up Ensign Rager, his phaser falls out of his holster. However, in the next shot, when Riker is back on the Enterprise, his phaser is clearly seen in its holster once again.
Dr. Crusher mentions having examined Geordi earlier 'today', then Data comes in to say that his self-diagnosis confirms that he was not on the Enterprise for a period of time 'yesterday'. But that period of time was after Geordi's first exam by Dr. Crusher.
Geordi puts the sensor relay emitter on the inside of Riker's arm at the crook of the elbow. When seen again in Riker's quarters, it is still on the inside of his arm, but closer to his wrist. After Riker is taken to the alien vessel. the emitter is on the outside of his forearm.
When giving Riker a recipe for a warm milk toddy, Dr. Crusher says "the heat activates the amino acids in the lactose, making it a natural sedative." Amino acids are organic compounds that make up fundamental biomolecules like proteins. Lactose is a simple disaccharide (sugar) molecule in milk that is not made of amino acids. Anyone with basic organic chemistry training would know lactose doesn't contain amino acids. Moreover, heating (to the temperature of warm milk) does nothing to the properties of amino acids and the expression "activates the amino acids" is meaningless anyway.
REM deprivation does not make a person feel tired (which is what happens to Riker here). The effects of REM deprivation are more accurately depicted in Night Terrors (1991).
In Data's Ode to Spot, he states "though you are not sentient, Spot..." Merriam-Webster defines sentient as "capable of sensing or feeling : conscious of or responsive to the sensations of seeing, hearing, feeling, tasting, or smelling" which cats and most other mammals certainly are.
During his poetry reading, Data reads his "Ode to Spot" incorrectly. He reads the first two lines as a question:
"Felis catus, is your taxonomic nomenclature/An endothermic quadruped carnivorous by nature?" But that reading makes no sense to anyone who actually understands those words. Those lines are properly written as a statement of fact:
"Felis catus is your taxonomic nomenclature/An endothermic quadruped, carnivorous by nature."
('Felis catus' is your scientific name, a warm-blooded, four-legged creature that eats meat.)
Captain Picard's opening log entry says that the Enterprise has entered a dense globular cluster, but all external shots of the ship in this episode show a normal star field with few nearby stars. Globular clusters have stars relatively close together. The external shots of the ship should have shown hundreds, if not thousands, of nearby stars.
This is incorrect. Globular clusters are *relatively* densely packed (astronomically speaking) and seem crowded from a distance. However, they can be up to 300 light years across and the stars may not seem that close together when you are in the middle of one.
When Riker sits at the conn, and runs his hand along the top edge, there are clearly very 20th century screws holding the console facing on.
At 0:36 to 0:48, you can see the camera in the far right edge of the mirror.
Riker is oversleeping and exhausted due to his nocturnal journeys into the aliens' realm, when he first arrives in Engineering. Then Geordi suggests modifying the warp field to increase their scanning speed. It is those modifications which open the hole into deep subspace, where the aliens are. None of the crew should have been taken by the aliens until after the modifications were made.
Considering an emergency has been called in, the cargo bay security and medical teams weren't exactly rushing to the scene.
With 5047 specifications of table in the database, the computer knows exactly what type of table to create in the holodeck based on very little information given by those taken by the aliens.
When the abductees are in the holodeck trying to recreate the table, they all agree that the table was inclined. When Riker is abducted at the end of the episode, we see two tables. While it's possible that the tables have been replaced, both appear level and wouldn't seem to support such functionality.
Data says he was off the ship for 90 minutes and 17 seconds. However, he then goes on to state that he was away from 12:54 to 14:26.
Even if he was away from 12:54:59 to 14:26:00 it would have been a minimum of 91 minutes and 1 second.
The crew are trying to determine the appearance of the table they were on by using the holodeck. Riker says the table was metallic, and Troi orders the computer to change the wooden table into a metal table. Although the computer does change it into metal, it also completely changes the structure of the table without having been asked.