Big-Lipped Alligator Moment: The naked woman who pops up on John Spartan's video screen in his apartment. He's just as confused, too. The novelization indicates the purpose of the scene is to demonstrate to him that video-calling is the norm in the future.
Complete Monster: Simon Phoenix, a psychotic criminal from the gang-ruled era of Los Angeles in the late 20th century, indulged in theft, kidnapping, rape, arson, and murder to his heart's content. He holds 30 people hostage and demands a ransom when in fact he had already killed them all, and frames John Spartan for their deaths. They are both sentenced to cryo-stasis and only woken up in 2032 when the new city of San Angeles has become a crime-free nanny state. Simon breaks out of confinement by gouging out a guard's eye to bypass the retinal scanner and indulges in his freedom to be a maniac and spread chaos again, brutally murdering almost everyone who gets in his way. It turns out he was unfrozen by the benevolent dictator Dr. Raymond Cocteau to assassinate Edgar Friendly, the underground Rebel Leader who has been trying to undo the oppressive system. Simon sets out on this task with murderous glee, killing many innocent bystanders in the process. He eventually teams up with his old gang after they're unfrozen and murders Cocteau to start a new lawless dystopia. He starts by unfreezing every violent criminal locked up in the cryo-prison, before gunning down all the technicians because he no longer has any use for them.
Do Not Do This Cool Thing: As noted by Cracked, while San Angeles is supposed to be a Crapsaccharine World, to a modern viewer it can look quite livable and prosperous, at least if you don't mind milquetoast. The reason the police are so helpless against Simon Phoenix is because they won: they succeeded so well that it's been years since crime was ever a problem, leading to complacency. It's especially apparent when you compare it side-by-side with the dystopian hellscape of near-future Los Angeles seen in the opening. Becomes less cool when the fascistic nature of the city becomes clear.
Looking through the Cryo-Prison inmate list, Phoenix exclaims "Jeffrey Dahmer? I love that guy!" In 1994, Dahmer was bludgeoned to death in prison; the line was subsequently cut from a number of broadcasts.
The name "Scott Peterson" comes up during Huxley's access of the parole hearings. Presumably, this is not the man who kidnapped and murdered his pregnant wife in 2003.
Spartan crashes the 1970 442 through the floor of an Oldsmobile dealership in 2032. Oldsmobile was discontinued by GM in 2004.
The seashells. They've supposedly replaced toilet paper, but are otherwise Noodle Implements, so many memes have sprung up about them.
Taken to a new level during the COVID-19 pandemic due to toilet paper shortages caused by people panic buying.
One-Scene Wonder: The "Fuck you, Lady!" girl from the old news report. Both for the line coming from a small child and that the line can be seen as a Take That! to people criticizing others from handling situations they deem as bad despite never being in similar situations.
When the future cop car was jumping through the SAPD sign, the letters and symbols were each engraved on a separate plate of glass. Just before the car hits it, all but one of the plates are pre-broken; the unbroken one has a broken one on the other side of it, making it obvious it wasn't the car that did it.
While it's more Makeup Failure, but keep an eye on Phoenix's Heterochromia. Several times in the film his blue and brown eye noticeably switch sides between shots.
When Simon's hideout is blown up at the beginning, you can clearly hear people in the background cheering at this extraordinary demolition.note While in-universe, it could be other criminals cheering at the destruction, in real life, it's probably the noise of onlookers or crew; they actually destroyed a real building for that shot, an old Power & Water in Los Angeles that was in fact scheduled for demolition at any rate.
Tastes Like Diabetes: San Angeles in the year 2032 is squeaky-clean to the point of absurdity, with commercial jingles from The '50s as the most popular genre of music and everyone relentlessly cheerful at all times. You're almost cheering Phoenix on, at least at first, if for no other reason than you want to see some chaos inflicted on this smiley, chipper city.
Zachary Lamb is the last cop on the force to really remember the bad old days, and is an old friend of Spartan, but he barely appears after Spartan is woken up, when his interactions with Spartan and Huxley could have provided a long and satisfying subplot to the movie. And it could have been worse; a deleted scene had him reappear later in the movie, only to be murdered by Phoenix.
They Wasted a Perfectly Good Plot: Given how the programming of both Spartan and Phoenix while they were frozen did have results it would have been interesting to see an actual felon who was reformed and made into a productive member of society that way (there's the piano singer at Taco Bell, but he's used only for a throwaway gag), and watch Spartan wrestle with the conflict between free will and a scumbag having been changed for the better.
The museum's 20th century weapons exhibit has functional and loaded weapons on display with relatively light security. Even discounting Simon Phoenix as an Outside-Context Problem for the setting, Edgar Friendly could have done a lot of damage if he'd ever decided to do a smash-and-grab on them.
Cocteau feels comfortable freeing Phoenix because Phoenix's conditioning prevents Phoenix from killing Cocteau... but Cocteau never considered that Phoenix could order someone else to kill him.
Spartan renders Huxley unconscious before the final battle even though she proved just a few minutes before to be quite a capable fighter (even saving Spartan's life) and probably would have come in handy during the final fight (The Nostalgia Critic actually did a run-down of all the possible things Huxley could've done to give Spartan an assist during the fight). Justified somewhat in that It's Personal between him and Phoenix. Afterward he explains he did it for her own good, and he may have been right; Phoenix was tweaked to be much stronger and deadlier than his mooks, and would have had no problem with killing her. Also she got rattled after killing one of Phoenix's mooks; it's possible that Spartan predicted his fight with Phoenix could only end in blood, and he didn't want to traumatize her further.
What Do You Mean, It's Not Political?: Some have described Demolition Man as being one of the most libertarian movies ever made. One of the film's villains is a scientist who has basically created the ultimate nanny-state, where everything deemed bad for you has been outlawed. And Edgar Friendly and his followers, who are initially portrayed as terrorists, turn out to be sympathetic freedom fighters who want to make their own decisions without the overbearing government's influence. The worst thing they do is steal some food and spray graffiti.
In all fairness, the graffiti is stated to be detonating graffiti, and we see small detonations on the spray machine, and that's just the result of small amounts of it being left on the spray nozzles, imagine what a full graffiti scrawl would have done.
For the pinball:
Complacent Gaming Syndrome: Some players will always select the "Freeze" award on the Cryo-Claw — it provides progress towards multiballs.
So Bad, It's Good: The promotional video for the pinball, which attempts to duplicate the atmosphere and special effects of the movie on a shoestring budget, while hyping up the game's gun grip controllers, all intermixed with actual film clips. It fails spectacularly, but has an innocent appeal, like watching an eight-year-old attempt to duplicate a Michael Bay film in his backyard.