Evil Is Cool: The titular killers in Hemingway's story were seen as archetypal bad guys with cool and witty slang. Lee Marvin and Clu Gallagher in the remake take this and run with it. This is averted however in Siodmak's original film, where the killers aren't charismatic but Ava Gardner's Femme Fatale most definitely is.
Take That, Scrappy!: Critics who generally dislike Ronald Reagan are rather fond of the 1964 film where Reagan is a corporate gangster, who also slaps around his moll. Even in 1964, Reagan as the vocally anti-communist head of the Screen Actor's Guild Union had a considerable number of critics.
Anvilicious: "Land of the Free" and the accompanying video takes aim at the illegal immigration argument with all the subtlety and nuance of putting a loaded shotgun to the Border Patrol's crotch and blowing their balls off. Considering that the music video is a Spike Lee joint, it probably comes with the territory.
Alternative Character Interpretation / Fridge Horror: "Bones" is not officially part of the murder trilogy, but consider this: it's about a guy trying to convince his girlfriend to go down to the beach with him at night, while "Midnight Show" is about a guy who takes his girlfriend to the beach at night and strangles her.
There's a different take on "Jenny Was A Friend Of Mine" in live performances. Sometimes the line "she couldn't scream while I held her close" is replaced with "she couldn't scream while I held her throat". Not always, but it's enough to imply the protagonist might not be the innocent man he claims.
Awesome Music: So much to list. "Mr. Brightside", "Read My Mind" and "Human" come to many minds, although the other songs are all good in their own right. "Run for Cover", "The Man" and the title track off of Wonderful Wonderful also qualify.
Epic Riff: "Mr. Brightside" accomplishes this almost instantaneously.
Germans Love David Hasselhoff: They're much more widely known and respected in the UK than their native America. "Mr. Brightside" is a club staple there and holds numerous chart records. It's reappeared on the list in every year since its 2004 release, and has spent over three years total on it.
The trend of "Mr. Brightside But..." and putting an awkward setting to fit the song's ironic lyrical themes to it's peppy beat. The best known one is "She left you last minute at prom so you're crying in a school bathroom while Mr. Brightside plays".
Nightmare Fuel: "Midnight Show" is about a Crazy Jealous Guy who murders his girlfriend and then goes driving around town with her corpse in the backseat, looking for a place to dump her body.
The video for "Bones", unsurprisingly directed by Tim Burton.
The closing rendition of "Silent Night". Also could double as a Funny Moment.
The message of "Mr. Brightside" is this combined with a Tear Jerker; the singer is apparently getting cheated on by his girlfriend/wife, and he knows it, but he doesn't really want to do anything about it because he seems to think that he either deserves it or isn't even worth the woman's time to begin with. Very existentially troubling, that.
Signature Song: "Mr. Brightside", with "Somebody Told Me" a close second.
"When You Were Young" and "Human" are widely recognized tunes as well.
Suspiciously Similar Song: "Runaways" uses a lot of the same chord progressions as "Heat Of The Moment" by Asia, especially the power chords at the end of the first chorus. Fitting, as both are more or less about the same subject.
Uncanny Valley: That... thing at the beginning of the Spaceman video. You know the one.
Oh, you mean the backwards-legged human-bodied horse-deer-thingy?