Artistic License Biology: The twin scientists in the sequel guess that Gizmo is some kind of rodent, yet he lacks the buck teeth that all rodents share; if anything, he looks like a prosimian primate.
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.
Second movie:
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 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.
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.
Gremlins + Atlantic Ocean. That is all.
An offhand radio broadcast in the first film implies that the Marines were going to hose down the gremlins if it weren't for Billy and Gizmo killing them all first.
Fridge Logic: How does a gender-flipping serum work on an asexual creature?
Hilarious in Hindsight: John Glover plays Daniel Clamp, an honest, likeable Millionaire who subverts many of the stereotypes about corporate executives. Ten years later, he played Lionel Luthor who may just be the trope codifier for the Corrupt Corporate Executive.
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.
Moral Event Horizon: Stripe is much nastier than the other Gremlins, who are typically mischievous in nature.
Woobie, Destroyer of Worlds: One particular Mogwai, stated as Earl in official media, is hinted in the film and novel as being one of the few Mogwai blessed with a more docile personality similar to Gizmo, that is until he is taken to the university to be experimented on and then happening on that sandwich, destining him as another psychotic Gremlin and to the same ill fate as all his other bretheren.