Base-Breaking Character: 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.
The battle against the Borg Cube showcased a large number of brand new Federation starship designs, almost more than the entirety of TNG. This includes the Akira Class, Steamrunner Class, Saber Class and Norway Class. That made them rather special to fans. The Akira class especially went on to become a major presence in Treklore.
Evil Is Sexy: The Borg Queen is horrifying and disgusting, but manages to be strangely sexy. Which makes it even worse.Roger Ebert commented in his review, "I also admired... the peculiar makeup work creating the Borg Queen, who looks like no notion of sexy I have ever heard of, but inspires me to keep an open mind."
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.
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.
On the commentary, Moore and Braga talk about how awkward it was to have to Retcon the Borg Queen into "The Best of Both Worlds," which gets them talking about how the decades-long continuity of Star Trek has become such a burden to its latter-day writers, and whoever takes it next would probably be better off just wiping the slate clean. In 2009, that's exactly what happened.
Anyone who has watched Star Trek: First Contact and the team X-Men films before Children of Dune finds it amusing that the Borg Queen is the grandmother of Professor X. (James McAvoy plays the younger version of Patrick Stewart's Charles Xavier.) By virtue of being a Kwisatz Haderach (a being who can access the genetic memories of its female and male ancestors), Leto Atreides II (McAvoy) has intimate knowledge of the Lady Jessica (Alice Krige) that he finds very uncomfortable, which mirrors Picard's distress that the Borg Queen knows everything about him when he was assimilated into her collective. Stewart also appeared in David Lynch's film version of Dune.
In Luke Cage, Alfre Woodard is the one who violently bludgeons someone to death as they lie helpless on the floor.
"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.
Jerkass Has a Point: Starfleet Command is portrayed as incompetent for not allowing Picard to lead the defense against the Borg invasion and indeed keeping him as far away from the battle as possible. However, considering what we see happen to Picard over the course of the movie, it's hard to say they were wrong. Having your battlefield commander undergo Sanity Slippage in the midst of an enemy blitzkrieg is a pretty good argument for wanting Admiral Hayes to lead instead.
Although, it doesn't justify keeping one of the most powerful ships in the fleet out studying comets along the Neutral Zone while Earth itself is threatened by the greatest enemy the Federation has faced - One wonders why they didn't just recommend Riker take command, given that he was in command of the Enterprise-D during the last Borg invasion.
Remember the Dominion was still a lingering threat, and the Romulans could been waiting for an opportunity like this to start trouble. As powerful as the Enterprise is, it's still only one ship to the many already gathered yet it'd be sufficient to provide security on the Federation borders.
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.
Picard's Big "NO!" (before he breaks his little ships) has also turned into something of a meme, even being referenced in South Park.
Picard and the machine gun.
The stardate given in the opening scene puts the film during an episode of Deep Space Nine where Sisko was away in the Gamma Quadrant. This has caused fans of his Memetic Badass status to insist the Borg are actually afraid of him, and deliberately waited until he wouldn't be around to stop them.
The scene where the crew depart via the escape pods would have looked more dramatic, if the escape pods didn't look like tiny pianos.
The franchise Title Drop that the crew is "on some kind of star trek." In the commentary, Moore and Braga reveal that the studio insisted on it, and they really didn't want to do it. They also considered Worf's "Assimilate This!" one-liner to be the cheesiest line of the movie.
A lot of the scenes with the Borg Queen seducing Data. Lines such as "That's because you haven't been adequately... stimulated" and "Was that good for you?" were particularly clunky. Sheeesh.
Picard's "The line must be drawn HERE!" speech is so over-the-top, particularly Picard's pronunciation of "here" as "HEE-YAH!", yet Patrick Stewart still sells it.
Cochrane's Title Drop can cross back into this, particularly since he's the "creator" of the Star Trek universe (and an awful lot like a thinly-fictionalized version of the real creator), and probably the only character entitled to do it!
Who else noticed that they completely forgot New Zealand? Maybe it was destroyed in World War III. And then rebuilt in the 24th century.
Earth's atmosphere looks oddly clear considering that the movie takes place during the post-atomic horror period of human history, in which TNG established there were multiple nuclear winters as a result of World War III and minor nuclear exchanges in the years afterward.
The lightning/plasma disc/plate on the Borg alcove, essential component of Borg technology related to the Borg's regeneration cycle and connection to the Borg hive mind, or cheap novelty item for your home? (Something of an inversion in that, while the "Luminglas" brand of crackle-tube widget existed prior to the film and the ones used in First Contact were bought off the shelf, it was their exposure in First Contact that made them popular as a novelty item, in sort of a proto-Colbert Bump effect.)
They Wasted a Perfectly Good Plot: The trailers played up the potential for an all-out Borg invasion (while saying nothing of the Cochrane subplot), which some fans might have wanted to see more than the story we got instead.
True Art Is Angsty: The darkest of all the TNG films, is also the most well-received, being the only TNG movie with a "fresh" score on Rotten Tomatoes.
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.