Big-Lipped Alligator Moment: The whole "Santa Claus" speech comes out of nowhere, and isn't mentioned again afterward, leaving it completely without any resolution. It has absolutely no reason to be in the movie other than to be disturbing. The sequel had some fun with this when it turns out Christmas isnt the only holiday she has traumatic memories about, but this time no one cares.
Cult Classic: For many reasons, but above all because of the nostalgia for the '80s and the very strong charm of the series. As an example, this film is considered a nostalgic classics, even in Eastern Europe or Asia.
Evil Is Cool: Stripe, probably the only gremlin in the film who's both totally evil and wickedly smart.
Harsher in Hindsight: At the end of the movie, the old Chinese man says (to the American family), "You have done with the mogwai what your society has done with ALL of nature's gifts!" Fast forward 30 years to the ecological nightmare that is modern China.... Mind you, this was something a Broken Aesop even at the time.
I Am Not Shazam: For the record, the main gremlin's name is "Stripe" not "Spike", and the lead gremlin in the sequel is officially named Mohawk (though Word of God suggests that they are indeed the same character, reincarnated).
Memetic Mutation: Thanks to this film, the word "gremlins" was primarily associated with its characters.note It was first invented by World War II pilots, who would joke that they were responsible for any mechanical failures in the aircraft. And the official theme, so much that many now remember it more than the film itself.
Narm: Kate's story about how her father died in the chimney as he tried to climb down it while dressed as Santa Claus may have been intended to be creepy and/or sad, but the simple absurdity of the situation can also make it a little hard to take seriously. (And the creators apparently recognize this and make fun of it in the second movie, where this time Kate starts narrating why she hates Lincoln's Day and she gets interrupted by Billy who tells her they don't have the time for it.)
Done intentionally. Word of God is that the scene is supposed to be emotionally complex, and the audience isn't supposed be sure whether they should be empathizing with Kate's tragedy or laughing at the absurdity of the situation. Intended to encapsulate the emotion of the film as a whole: are the Gremlins nightmare monsters who cause carnage, destruction, and death everywhere they go, or gleeful live-action cartoons just being silly?
Special Effects Failure: There's a few times where one can see the hand of the puppeteer. In particular, the rod in the arm of the plate-throwing gremlin in the kitchen attack is clearly visible during the over-the-shoulder shots.
Suspiciously Similar Song: All video games of the franchise use an off key version of the main theme. Subverted with The New Batch for Amiga and Atari ST, which uses genuine arrangements of the film's soundtrack (plus the Gremlin Rag from the first film).
They Wasted a Perfectly Good Character: The first movie bothers to properly introduce several residents of Kingston Falls, even giving them detailed personalities and backstories. Most of them disappear in the second act or end up quick victims of the Gremlims' rampage. It's especially glaring with Gerald (played by Judge Reinhold) who is set up as a jerk deserving of some comeuppance — and is then never seen again after his second scene in the tavern (though he is terrorised in a deleted scene). The sequel seems to go out of it's way to avoid the same mistake, even bringing back a handful of the original cast to be utilised more fully.
What Do You Mean, It's Not for Kids?: This movie, along with Indiana Jones and the Temple of Doom led to the creation of both the PG-13 rating in the USA and the 12 rating in the UK. The trailers presented this picture as much more lighthearted than it was. Reviewing it for Isaac Asimov's Science Fiction Magazine, Harlan Ellison described it in terms more suited to Nightmare Fuel. He deplored its many instances of wanton cruelty played for laughs, and said he "heard little children scream and cry" in the theater. The manager later told him he'd never had so many patrons walking out and demanding their money back.
The Woobie: Gizmo in both films, being abused by his spawned offspring, taken from Billy and Mr. Wing dying in the second film. And then the mad scientist cages Gizmo to start the whole mess all over again.
Iron Woobie: Despite all this, Gizmo remains a cute, cuddly, friendly little critter, with genuine affection for most of the people he meets, but especially Billy and Kate. And in Gremlins 2, after being pushed too far, he Takes A Level In Badass.