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.
From the soundtrack, Only Myself to Blame by Scott Walker. It was to be used in the film's end credits, but was unfortunately decided to be too glum a note to go out on.
Ensemble Darkhorse: Say what you will about this film's faults, but few can deny it created a fantastic character in Elektra. She's typically found near the top of people's Bond woman countdowns, and amazingly enough accomplishes this without really having any "iconic" scenes like Ursula Andress or Honor Blackman did.
"Funny Aneurysm" Moment: This was Desmond Llewelyn's last appearance as Q in the Bond movies. He died in an auto accident shortly after the movie's premiere, and his last scene shows him descending through the floor on an elevator with a car. Ouch.
VHS home editions of the movie lampshaded this with a tribute to Desmond Llewelyn.
Even then, it was one hell of an exit. Q left in style.
He's Just Hiding: Valentin, not helped at all by the DVD commentary saying on the subject, "It's only a flesh wound!" Of course, since the character did not appear in Die Another Day, and since the series was subsequently rebooted, it will never be known if Zukovsky in this continuity could have ever come back.
"That era of the franchise addressed the anachronistic aspects of the character, portraying Bond as a flawed, morally ambiguous throwback to an older era, almost a man out of time. This approach of self-awareness had mixed results. It certainly helped give older fans a taste of what they’d been missing in their Bond movies, but it wasn't very forward thinking, as it did little to adapt the franchise to its modern setting. It was merely a stall tactic."
Narm: As listed in the Funny section, the scene where Bond learns from Renard that Elektra just might be behind it all would probably be a bit more dramatic if Bond didn't audibly say "HUH?!" with a hilariously dumbfounded look on his face.
Brosnan's overstated performance in other scenes gets it fair share of mockery as well. The scene where he confronts Elektra, specifically his lines, "Knew all about my shoooulder; knew exactly how to huuurt me," stands out, as does his "pain face" when being garroted by Elektra.
One-Scene Wonder: The Cigar Girl assassin. The director wanted her for the role of Elektra, but upon realizing that her English wasn't up to par, he gave her this part instead. With only a few minutes of screen time and exactly two lines, she manages to be one of the more memorable minor Bond Girls—her panicked, terrified response of "Not from him!" (when Bond offers to protect her) just before she kills herself is enough to provide an intriguing hint about just want kind of monster is Bond dealing with.
The Scrappy: Dr. Jones and Mr. Bullion. On the non-human side, Bond's BMW. (In GoldenEye, it's never used at all; in Tomorrow Never Dies, it's crashed through a window from a great height; in this, it's sawn in half!)
Strangled by the Red String: While one can hardly expect a relationship between Bond and his current Bond Girl to have any real substance, his fling with Christmas Jones is a glaring example of this. They have absolutely zero romantic interaction or flirtation (shockingly absent for a Bond film) before hooking up in the movie's final scenes. Her sole purposes in the film seems to be to completely botch Bond's first attempt to stop Renard's plot (making the second half of the movie her fault alone), and for Bond to have a warm body to be in bed with once Elektra is revealed as the villain and Bond kills her. Made all the more jarring by the fact that he does have chemistry with Elektra, and it's even implied that she's one of the few women he's considered settling down with which unfortunately ceases to be an option by the end.
Tear Jerker: Valentin's death. Renard's may count as well.
Also Q's farewell on a meta-level. It doesn't help that Bond, for a split second, looks positively grief-stricken as he asks Q if he really plans to retire soon.