These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Base Breaker: The Borg Queen, also goes for her appearances on Star Trek: Voyager. Some find her an interesting addition to the Borg. Others believe her creation was a huge mistake, going against everything the Borg embody.
Genius Bonus: The opera that Picard is listening to is Hector Berlioz' Les Troyens. The song is "Hylas' Song" from the beginning of Act V. Hylas is a homesick young sailor being rocked to sleep by the sea as he dreams of the homeland he will never see again.
Hilarious in Hindsight: Picard gets accused of acting like Captain Ahab. Guess what role Stewart would play two years later?
As he first meets Riker, Cochrane asks Troi "Is he a friend of yours?", to which Troi answers "Yes.". He also asks "Husband?", to which Troi says "No.", making him say "Good!". In Star Trek: Nemesis, Troi and Riker finally marry.
Holy Shit Quotient: The opening battle against the Borg ship. That sequence alone was worth the movie format. Especially when the Enterprise fires the blue quantum torpedoes the surround sound crushes you into the chair.
Inferred Holocaust: The Borg's assimilation of the Enterprise must have led to the deaths of hundreds of Enterprise crewmembers, both those who were assimilated and those trying to fight them off, as well as major damage to the ship, especially in Engineering.
Like You Would Really Do It: Destroying the Enterprise-E. Its predecessor had been destroyed in the previous film and the characters even Lampshaded how short the ship's lifespan had been. Of course they weren't going to get rid of it right away.
Who else noticed that they completely forgot New Zealand?
They Wasted a Perfectly Good Plot: The trailers mentioned little to nothing about the Cochrane subplot, instead playing up the prospect of an all-out Borg invasion. That could've been as good, if not better, than what we got.
And this movie isn't half-bad, so that's saying something.
Still, they averted a potentially much worse case of this trope. The original screenplay was role-reversed and had Picard impersonating the injured Cochrane, while Riker fought off the Borg invasion. The focus of the story was Picard's wacky antics while pretending to be Cochrane, and in the end he never even found out that the Borg had ever been on the Enterprise. Thankfully Patrick Stewart stepped in and pointed out that it would be about a million times more logical to follow up "The Best of Both Worlds" and have Picard confronting the Borg once more.
Also, Sisko should have been in this movie. He would've been a good counterpoint to Picard, especially since they've both been hurt by the Borg.
SF Debris joked that the Borg deliberately waited until Sisko was away from the station and the Defiant to launch their attack. The stardates even work out.
Unfortunate Implications: The film suggests that even though humans created warp drive on their own, the real reason humans got out of darkness and became great was because visitors from the sky came down and made us that way. Disappointing when you remember Gene Roddenberry hated such tropes as Ancient Astronauts.
Star Trek: Enterprise showed that it wasn't that simple: humanity spent the next 150 years fighting and scraping for every step forward, with no assistance (indeed, active resistance) from our strongest 'ally'. Remember, it took over a century to develop the Warp 5 engine, and another 30 years after that to get it up to Warp 7, with all of that progress being made in the face of the Vulcans holding humans back. First Contact with the Vulcans merely showed humanity that we weren't alone, and inspired us to go out and see what else was waiting outside our own little corner of the cosmos.
Villain Decay: While it works in this movie, the introduction of the Borg Queen marks the start of the Borg's overall decay, since even Data notes that the very existence of a Queen challenges previous assumptions about how the Borg work. Apparently earlier drafts of the script didn't have the Queen, but they realized that the Borg were essentially cyborg zombies without some sort of leader.
It works in this movie because the queen doesn't actually violate any of the rules the Borg are set up by, it's just very obtuse about it, and she is very obtuse about it in-universe, hence Data's confusion. Her "I am the Borg" spiel would imply she's simply the collective expressed through a single voice, no different than the disembodied voice speaking to Picard in "The Best of Both Worlds;" hence why he remembers her and says "you were there all the time," and why she laughs in his face when he questions how she can be alive when that ship was destroyed; the destruction of that ship didn't put a dent in the collective itself, it only destroyed the body the collective was using to express itself on the ship. She's basically outright saying as much, with Sesquipedalian Loquaciousness, when Data asks if she "controls the Borg Collective and her reply is "You imply a disparity where none existsnote in other words, "you're suggesting there's a difference between myself and the thing you're asking if I lead,"; I am the Collective." It also makes the Borg altogether creepier to think about as a massive all-encompassing Hive Mind that, unlike most examples of the trope, is in itself an individual with thoughts, goals and concerns beyond insect-mentality reproduction. It doesn't work in Voyager because in Voyager these statements are directly contradicted. The queen is shown conversing with and giving orders to the disembodied voice of the collective, which suggests the exact opposite, that she is a separate entity leading it.
Visual Effects of Awesome: Many examples, including the battle at the start, the assembly of the Borg Queen, and the spacewalk on the hull of the Enterprise. Unfortunately the producers ditched ILM starting with the next film, meaning that the visual effects in this film wouldn't be surpassed until they were called back for Star Trek XI.