Audio problem: In Engineering when Worf says "Ensign," Michael Dorn's lips don't move. (00:22:35)
Visible crew/equipment: After the encounter with Borg in main engineering, when it cuts to the observation lounge with Guinan participating in the conference, at the start of the first shot you can see the shadow from the camera and crew person as it moves, at the bottom of the screen. (00:24:10)
Other mistake: Worf says the Borg have locked on a tractor beam, but in the next exterior shot there is no tractor beam visible between the two ships. Later there is.
Suggested correction: Stating that it is locked on is not the same as stating it is engaged. For example, there are numerous occasions where they detect that phasers have been locked but have not yet been engaged/fired.
In regards to a tractor beam, locked on has always meant engaged and holding the target. Phasers are different as they need to be targeted. The tractor beam just has to hit the ship. I think this is a valid error.
Other mistake: As Guinan sits at the desk, she reaches toward, but doesn't touch, the control for the screen, but it activates.
Continuity mistake: In the Shuttle, Q's hair is arranged in bangs on his forehead. A split second later in Ten Forward, his hair is up and back from his forehead in the familiar style.
Suggested correction: Q's powers has shown in the past that he can change his looks in an instance, as well as his location and anyone else he chooses. This is precisely what happens here.
Continuity mistake: When the security man gets tossed by the Borg, as he lands and rolls next to the far wall, his phaser falls out of the holster, and lands next to his shin. A second later, it's about two feet away from his leg.