Inverted - At one point, Lily calls Picard "Captain Ahab" in reference to his personal vendetta against the Borg. Patrick Stewart was so pleased with this scene that he went ahead and played Ahab in a made-for-TV movie version of Moby-Dick.
Beam Me Up, Scotty!: Picard actually misquotes Moby-Dick. The change is obviously to simplify the text for modern audiences by putting it into more modern language. There are three possibilities: in the future, someone has revised one of the greatest novels of all time, Picard's exhausted and either misremembering or paraphrasing the quote, or Picard's translator gives it in modern English for Lily rather than the original language.
Picard: “And he piled upon the whale's white hump, the sum of all the rage and hate felt by his whole race. If his chest had been a cannon, he would have shot his heart upon it.”
Original: “He piled upon the whale's white hump the sum of all the general rage and hate felt by his whole race from Adam down; and then, as if his chest had been a mortar, he burst his hot heart's shell upon it.”
Ira Steven Behr insisted that the "tough little ship" exchange be added to the opening battle, so it was clear that the Defiant had survived and could still be used on Deep Space 9.
When discussing what the next TNG movie should be about writers Brannon Braga and Ronald D. Moore wanted to do a movie featuring the Borg while Producer Rick Berman wanted to do a time travel movie. Their solution? Do both!
Older Than They Think: The concept of a Borg "Queen Bee" is an old one; it goes as far back as "The Best of Both Worlds". However, the writers decided that the Borg were so effective precisely because they lacked leadership. Thus, Picard (Locutus) became the "Queen Bee".
A scene with Sisko ordering Worf to command the Defiant in the battle was to be featured. It was filmed, but cut.
Picard and Riker's roles were to be switched, and more emphasis was going to be placed on the Earth storyline. Part of the reasons for the switch were apparently because Patrick Stewart felt Picard should have more of an active role in defending the Enterprise, while Jonathan Frakes wanted to have more time to focus on directing. Picard was also the one who had been assimilated by the Borg, so it made more sense for him to be the one to confront them.
The Borg Queen wasn't in the early drafts of the script. They started to formulate the character when executivescript notes remarked that they were just cyber-zombies and the movie needed a more tangible villain.
The Defiant was outright destroyed in one draft of the script. Unsurprisingly, the DS9 staff objected to what effects this would create for their show, so it was changed. (Incidentally, the ship would be destroyed on DS9, but not for another 2 and a half years.)
Tom Hanks as Zefram Cochrane. "Life is like a box of Gagh..."