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.
First movie: The whole "Santa Claus" speech in the first film comes out of nowhere, and has absolutely no reason to be in the movie than to be disturbing.
Though if you listen closely about almost mid-way in the movie (it is easy to miss), she does mention she hates Christmas, and so she told the story about why she hates Christmas.
It does, however, nicely adhere to the theme of trying too hard to make Christmas great (as Billy's dad did,) with a result of horrible consequences.
Firstly, there's the sequence at the beginning where Daffy Duck takes over the Warner Brothers logo from Bugs Bunny, attempts to move it back into place, and then ends up with it around his waist.
Later, while Billy is heading to the Clamp Building, policemen in body armour armed with rifles escort an armoured van, which opens up to let out mimes. This is given absolutely no explanation whatsoever and has no relevance to the plot.
When the conversation between Dr Catheter and Billy begins to skip, slow and distort, then revealing Gremlins in a theatre showing the film playing shadow puppets. A woman with her daughter comes out to complain to the theatre manager, then the projectionist, looking bruised and bloodied, comes down, stating he is not performing that task without heavy compensation.Then, the theatre manager goes into the theatre and speaks to a patron, who turns out to be Hulk Hogan, and manages to get the movie running again by threatening to beat up the pesky Gremlins.
For the home versions, the scene was replaced with a similar bit where the Gremlins ruin the tape the viewer is watching. This prompts John Wayne to gun down a few of them and return us to our movie. "I don't need varmints on my ranch, and you folks don't need them in yer TV set.
And finally in the novelisation, the Brain Gremlin locks the author out of his study and swipes his typewriter, briefly taking control of the narrative until taking off when the author takes a fire-axe to the door.
Chaotic Neutral: Greta, she's more interested in inspiring chaos than doing chaos via competition of love interests.
Fridge Horror: What would have happened if each of the Gremlins took the Sunblock solution? (Pun not really intended.) This could also count as Fridge Logic directed at the Brain Gremlin for not even considering the idea after injecting it in Bat Gremlin.
Harsher in Hindsight: At the end of the first 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...
Ho Yay: Between George and Lenny.Then again,all Gremlins are asexual...
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).
Lawful Evil: Brain Gremlin, he is vey disciplined and believes by civilizing the Gremlins that they can gain enlightenment, though he still engages in For the Evulz at some points.
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.)
No Problem With Licensed Games: The NES game adaptation of the sequel by Sunsoft is fondly remembered for its active gameplay,its faithfulness to the movie it was based on and its amazing soundtrack as well as its advanced graphics.
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.