On Stardate 32611.4 (2353) the Hansens received approval from the Federation Council on Exobiology to begin their search for and study of the Borg - twelve years before the Federation knew of the Borg's existence. The Enterprise's first encounter with the Borg was in Q Who (1989) on Stardate 42761.3 (2365). Also, Janeway has previously described the Hansens as wanting nothing to do with Starfleet or the Federation.
When the U.S.S. Raven detects a Borg vessel coming after them, it is at warp speed, yet when Annika Hansen's father talks to her in her cabin, the stars outside do not move.
The Borg queen tells Seven of Nine that she is the first Borg to achieve individuality. In the Next Generation episode, I Borg, a drone was separated from the collective and achieved individuality. It took on the name Hugh before being re-assimilated. It's individuality infected the cube and caused its destruction.
Annika Hansen mispronounces 'assimilation,' saying "a-simulation," but then she's a 6-year-old child. Such difficulty with big words can be expected at her age. She also struggles with the word "cybernetic," though she just manages to pronounce it.
In one shot of Voyager near the beginning of the episode, as the ship passes by the camera, only one of the impulse engines is active. The one on the port warp nacelle pylon is not lit.
Material from the holodeck simulation of the mission to the Borg cube is re-used for the actual mission, including Janeway and Seven at the warp coil and Harry Kim and Tuvok at the shield emitter. This is a sensible time saver for the show's makers, especially because the Voyager crew should have the mission so down pat that two run-throughs would look nearly identical. But on the other hand, the crew themselves say the run-through was too long, and therefore they would act slightly differently during the mission. Also, reused material has Tuvok giving Kim orders on where to place explosive charges, which by that point Kim would already know.
When Captain Janeway is showing Naomi Wildman the communiques from the Borg to Seven of Nine in cargo bay 2 there are 3 distinct communication times between the Borg and Seven of Nine shown on screen. However only 1 communication is shown on screen in cargo bay 2. The other communication was on the sphere during the raid. So only 2 communications were made, not 3, and one of the 2 weren't even near cargo bay 2.
When the away team is on the sphere just before the shield matrix is destroyed it can be seen that Janeway doesn't have her bio dampener on her left arm as she is setting up the transport enhancer. Clearly a mistake by the show runners by not showing it because the only time it's shown she doesn't have it on is when she is in the holodeck.
The Voyager crew uses assorted devices (lifesigns inhibitors, multiphasic shielding, etc) developed by the Hansens to evade the Borg. However, the Hansens were assimilated by the Borg 20 years earlier, and the Borg should have known about/adapted to all of those devices.
When Captain Janeway plans to raid a damaged Borg sphere, she asks Seven of Nine to read through her parents' extensive logs and notes for the years that they studied a Borg cube, which they salvaged from the wreck of the USS Raven; however, the only crew that visited the Raven were Seven and Tuvok. Though Tuvok did have a tricorder with him, he was more concerned with escaping the wreck since the Bomar were shooting at them. They eventually escaped, and Paris beamed them up to his shuttle. On Voyager, Janeway directed the ensign at conn to leave Bomar space at warp 8 as soon as Paris had docked his shuttle. There was no time for them to have downloaded the Raven's logs, which were voluminous as evidenced by the number of data nodes that Nelix needed to fill.
As the landing party enters the bridge and Janeway tells Chakotay that Seven chose to stay behind, the shadow of a boom mike if visible above the door.
The Borg Queen says that Seven is the only Borg to return to a state of individuality. Either this is a deliberate or convenient deception, or she is unaware of the recurring characters 3rd-of-5 ("Hugh") and Locutus (Captain Picard's alter ego) from Star Trek: The Next Generation (1987) and the colonists from Unity (1997), although it is conceivable she was unaware of the latter.
After many dry runs on the holodeck for the away mission aboard the Borg sphere, Tuvok should not have had to tell Kim where to put the three spatial charges on the Borg shield, but he does.
Multiple references are made to Seven having been freed from the Borg for two years or more. By this episode, it would have been about 18 months (a year and a half), not two years.