After meeting Q's successor, Bond says "You're not leaving any time soon... are you?" It's subtle, but you can tell that Bond is saddened by Q's impending retirement.
And then you remember the scene, whether intended as that at first or not, eventually became a real-life sendoff for Desmond Llewelyn, who had played the character for thirty-six years, almost the entire run of the series up to that point, due to Llewelyn's death shortly after the release of the film in a car accident.
His last words in the scene plus the way he leaves by secret elevator deserve an honorable mention.
Q: I've always tried to teach you two things. First, never let them see you bleed.
Bond: And the second?
Q: Always have an escape plan.
During Bond and Renard's face-off in the underground nuclear test site, Renard taunts him by threatening to have Elektra killed. This alone causes James to fly into a fury, knocking out the semi-invincible Renard with the butt of his P99, and he growls while doing this. While James made some effort in the past to protect his female companions, his animalistic behaviour here shows just how much Elektra grew to mean to him. He makes it clear that no one hurts his woman while on his watch. Which makes it all heartbreaking when it turns out that Elektra was not really James', but Renard's woman. And it's James who has to kill her in the end.
It's twisted, but there's a decidedly WAFFy quality to Renard and Elektra's scenes together. It's fairly easy to forget you're watching a spy flick rather than a romantic dramedy, and that the two people onscreen are brutal terrorists whose relationship is seriously screwed up on almost every level.
Renard's death also, in a strange way. Elektra is killed prior, who was basically the reason Renard was doing what he did. When Renard is fatally wounded, Bond looks him in the eye and says 'she's waiting for you!', before delivering the killing blow. But after he says that line, Renard actually smiles softly and Bond nods to him, realising that yes, he's failed, but soon he'll be with Elektra again, and that means everything is going to be okay. It's a short but touching moment that speaks volumes about their relationship.
Valentin Zukosky is willing to use his last breath bullet to break Bond out of his restraints and sacrifice his chance at getting revenge on Elektra King.
As ridiculous as Christmas Jones is, from her actress to her name, it is at least heartwarming to see that, in her first meeting with Bond, he goes out of his way not to make fun of her name. Considering Bond's natural habit of making puns whenever possible, it's actually quite sweet to see he understood that she heard a lot of jokes about her name, and deliberately didn't make any at all.
Christmas Jones: Doctor Jones. Christmas Jones, and don't tell me any jokes, I've heard 'em all.
Bond: I don't know any doctor jokes.
The tribute montage of Desmond Llewelyn following his death in 1999 featured in home video releases of the film.