During the first fight against the Borg, the Borg adapt to the Starfleet phasers rather quickly. Worf's "Captain, they've adapted!" would sound slightly fearful when said by a member of any other species. Worf? Hell no. He takes his rifle and starts clubbing the Borg drones with it.
During the battle at the deflector dish the Borg again adapt to the phasers. This time, Worf slashes it apart with his beloved Klingon Mek'leth. When it manages to cut a hole in his suit, he patches it with the Borg's cables. Complete with trailing arm!
Hell, just the fact that the Klingons managed to create a melee weapon that can harm the Borg.
Picard is going blind with revenge against the Borg and calls Worf a coward for falling back and destroying the Enterprise. Worf stands up to him, face to face, and says with as much restraint a Klingon can have, "If you were any other man I would kill you where you stand!"
Another for Picard and his effect on Worf — there are precisely three men in the universe that Worf would let insult him like that without violent retribution. One is his son Alexander. Another is Picard. (The other is Sisko, but sadly, his only scene in this movie was cut.)
Special notice to the part when the the Phoenix launches (complete with its own Crowning Music of Awesome) and flies away from the Earth with the Enterprise in pursuit, while at the same time Picard looks utterly screwed ... until suddenly Data reveals his hand and breaches the coolant tank.
The Phoenix has another CMoA as it reaches orbit. At first it just looks like this rickety, cobbled-together thing that's barely a step up from a 60's space capsule... Then the side panels come off, and slowly a pair of Star Trek-style warp nacelles unfold and lock into position. And that is when the discerning Trekkie knows epic-ness is about to ensue.
Another for both Zefram Cochrane and Steppenwolf: Cochrane launches his modified nuclear missile to go to warp flight and get the attention of the Vulcans, leading to Earth's first contact with an alien race ... and he does it while blasting "Magic Carpet Ride" across the whole base.
First Contact itself, especially as the aliens are revealed to be Vulcans.
A subtle one for Starfleet comes up just after the Enterprise rescues the Defiant survivors — it might not have been enough, but even before Picard and the Enterprise's intervention, Starfleet was doing much better than they did at Wolf 359 six years earlier (compare 'light damage' to 'heavy damage to outer hull, fluctuations in cube power grid detectable to Starfleet sensors'). Further, Starfleet was able to keep up a running battle all the way to Earth's solar system; there were a lot of ships still going by the time the Cube reached Earth (compare "The Best of Both Worlds", where there weren't any ships left after Wolf 359 except the Enterprise, which, as here, arrived late) The Borg aren't the only ones capable of adapting...
This works as an example for the Borg too. Even with far more preparation and advanced ships, Starfleet still doesn't even manage to slow the Borg down. They come within a hair's breadth of reaching Earth. Oh and destruction of the Cube? The Borg are prepared for the eventuality too. There's a reason everyone in the Star Trek universe fears the Borg.
The leitmotif that plays when the Defiant and Worf are introduced? The Klingon theme, first heard in The Motion Picture when another looming menace was approaching Earth. And by this point in the franchise, that song had long since evolved to be a theme of imminent ass-kicking.
The Borg Cube's first scene. A giant 3x3x3 kilometer cube of twisted mechanical monstrosity looming over the POV, accentuated by a very loud four-note bass brass instrument chord, signifying newcomers and reminding longtime fans that the Borg are terrifying. Followed by Starfleet's incoming fire slamming into it. The Borg are a nigh-unstoppable force, but Starfleet is notgoing to go quietly.
Heck, the entire Battle of Sector 001 is one long Crowning Moment of Awesome beautifully married to Visual Effects of Awesome. And it all culminates when Picard orders every ship left to concentrate on the Borg's hidden weakspot, raining absolute barrages of phaser fire and photon torpedoes, capped off with the Enterprise-E's newest quantum versions delivering the finishing blow.