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.
YMMV: Star Trek: First Contact
Alternative Character Interpretation: Can Picard really hear the Borg despite having no implants, or is he just imagining it and his actions are based on his knowledge of them, not a direct connection? This makes him hearing Data unintentionally funny, since it's as if Picard just remembered that he had been captured after setting the ship to self destruct with him on board.
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.
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.
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.
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.
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.
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.