Admiral Paris' rank pin shows three pips, but in all other appearances, before and after, he has four.
Counselor Troi chastises Barclay regarding how inappropriate it is that he followed his therapist on vacation. In her previous appearances, she emphasized that they were more than counselor/patient, but genuinely friends.
When the errant escape pod approaches the Ferengi ship, the Ferengi frantically call out to "raise shields." As the Ferengi were operating their ship within the corona of a red dwarf star, their shields would already need to have been raised or they would have been vaporized.
Reginald tells Seven that she is the only Borg to regain its humanity. He overlooks Captain Picard who was assimilated by the Borg to become Locutus in The Best of Both Worlds: Part 1 (1990) and regained his humanity in The Best of Both Worlds: Part 2 (1990), an incident which Seven has discussed before.
However, the fact that Picard was assimilated by and returned from the Borg is quite probably a military secret that only command-level officers are aware of, and certainly not the Ferengi. In "Star Trek: Lower Decks", Lt. Steve Levy's conspiracy theory suspects that the Battle of Wolf 359 was an inside job, which it certainly was because Picard's knowledge was used to give the Borg an advantage.
However, the fact that Picard was assimilated by and returned from the Borg is quite probably a military secret that only command-level officers are aware of, and certainly not the Ferengi. In "Star Trek: Lower Decks", Lt. Steve Levy's conspiracy theory suspects that the Battle of Wolf 359 was an inside job, which it certainly was because Picard's knowledge was used to give the Borg an advantage.
When Voyager flies toward the screen at warp, it has obvious battle damage and is a reuse of footage from "Equinox Part II."
In the final scene, Barclay slightly stuttering as usual says to the computer, "C-computer, deactivate Broccoli program", using his old TNG nickname. The other characters don't notice, so it's clear it was meant by the actor to be an inside joke for the audience. The subtitles, however, spell his correct name "Barclay".
Harry says the transceiver isn't designed to handle photonic data; however, data is data no matter the contents. The Doctor has already been sent and received successfully in Life Line (2000), the previous Barclay story.
Commander Harkins suggests that the sending of the hologram to Voyager failed because its complexity led to signal degradation. In previous instances, the Doctor's program was sent back and forth with no problem, and in fact was sent to the USS Prometheus specifically because a holographic matrix is more stable than a standard data transmission.
Troi continues to express skepticism at Barclay's thoughts and insights regarding the Ferengi plan to steal Seven of Nine's nanoprobes even after he was vindicated in his belief that there was a plot to interfere with Pathfinder's transmissions and misappropriate his hologram.
Commander Harkin tells the visiting school children that the Pathfinder office is where their "homework" gets done. Homework is, by definition, work that is taken home, not worked on in an official setting such as a school or office.
The Voyager crew is delighted by the Reg hologram's "impressions" of members of the senior staff. As a hologram, he can be programmed with the vocal pattern of any individual. Doing impressions of the staff would not be much of an accomplishment.