In the first scene that is a direct continuation of The Best of Both Worlds: Part 1 (1990)'s cliffhanger, Dr. Crusher's hairstyle changes significantly from the scene in the previous season. It is a much fuller and thicker wig that is also less bright red.
The Borg cutting beam is shown striking the engineering hull, and the computer warns that it has created hull breaches on decks 23-25. The same footage was used in the prior installment and the hull breach was said to be on deck 36, which contained main engineering.
The exterior view of Picard looking out the ready room window does not conform to the shape of the exterior of the ship.
When Data and Worf take a shuttle to rescue Picard, they leave the saucer section via one of its shuttle bays. Through the port side windows, it's seen that they pass the warp drive section before they approach the Borg cube. This arrangement makes it appear that the shuttle left the saucer section from the front side. However, the shuttle bays are at the back of the saucer. There was no footage of them turning 180 degrees to head towards the cube.
In previous episodes the Battle Bridge looked different, and the Enterprise was slower than Borg ships from Q Who (1989). It is reasonable to assume that their technology and equipment were upgraded since then, in response to the earlier episode's events, to keep up with the "arms race."
Picard's skin is meant to have been tinted white as part of his transformation into Locutus. However, his hair is thin enough that his natural skin tone can clearly be seen through it.
When the Enterprise is first able to get a visual on the aftermath of the Battle of Wolf 359, the camera swoops through and around the wreckage in a dynamic movement. This would not be possible from the vantage point of the Enterprise, which was still approaching in a straight path at high warp speed. It would only be possible with a movable camera within the field of battle itself.
While Locutus is in Sickbay, he states, "You underestimate us, if you believe this abduction is any concern." Then, two statements later, he states, "I will continue to speak for the Borg, while 'they' continue without further diversion to Sector 001, where 'they' will force your unconditional surrender." His pronouns changed from us to I and they, causing an in-continuity. As part of the Collective, his pronouns should have stayed with the us, and we, rather than they.
However, it is established that he is called 'Locutus' because he (individually) will speak for the Borg and communicate with Earth/Starfleet/the Federation.
Riker mentions to Worf that Wesley was working on a type of chip to tune their phasers to different frequencies to counter the Borg being able to adapt and create force fields. Yet, previously, in "The Arsenal Of Freedom", Data was able to diddle around with his phaser to find a frequency that freed Riker from a force field.
We see the Borg ship approaching Saturn from the side of the planet illuminated by the sun. This would mean the Borg are actually moving away from Earth rather than toward it.
In every view of Earth, no land masses are visible.
Shelby tells Riker that the Borg have entered sector 001, and the next shot shows the cube-shaped ship nearing Saturn. That means that the enemy have already passed Pluto (still officially a "planet" when this show was made), Neptune and Uranus, all of which would have been part of the same sector. The Borg would have actually entered sector 001 approximately 2.8 billion miles sooner.
Admiral Hanson said that the nearest help for the Enterprise, when they first expected to encounter the Borg in part 1, was 6 days away. Yet Starfleet was able to amass a fleet of 40 ships at Wolf 359, later said to be 18 hours from where the Enterprise encountered the Borg, before the Borg cube arrived.
Early in the show, when the crew are reporting to Admiral Hanson over subspace from the Ready Room, Admiral Hanson calls Lieutenant Commander Shelby 'Lieutenant'. The proper abbreviation for her rank is Commander or the rank is said in full.
When Data informs Riker that the Enterprise is approaching Wolf 359, he pronounces it "Wolf three-fifty-nine." All other characters pronounce it "Wolf three-five-nine." Data, of all characters, would not be the one to alter a generally accepted designation.
Commander Shelby says that an outpost went offline at "twelve hundred hours thirteen minutes." The word "minute" is not used in military time. It should have been "twelve hundred thirteen," "twelve hundred thirteen hours," or even "twelve hundred one-three."