Revealing mistake: When the cops watch the guy in the Santa costume being attacked their brakes are cut under the car but a few moments later when they drive off down the street they do apply the brakes to stop from the lights exploding above and the brakes do work.
Suggested correction: A cut brake line would not stop the brakes from working instantly. It would take a few pumps of the brakes for fluid to expel. So the brakes would work for a little while.
Continuity mistake: When Rand Peltzer is in the gas station office with the gas station attendant, the view from the outside looking in shows the station attendant taking a drag off a cigarette with his left hand, but the next scene shot shows his left hand on his desk and reaching for a cigarette tucked in his right ear with his right hand.
Revealing mistake: When Stripe spits at Gizmo who was playing the trumpet, check for a little Gremlin behind lying down. When he raises his back a big hole is visible where the puppet is moved.
Continuity mistake: In the department store, Stripe is throwing radial saw blades at Billy, and decapitates a store mannequin twice. Further, the separated head falls off the body twice.
Continuity mistake: When the gremlins are driving Mr. Futterman's snowplow towards his house, it comes to a stop, but the next shot from the perspective of the gremlins in the cab show it still moving.
Continuity mistake: The fan the Gremlin is swinging on changes direction between cuts.
Continuity mistake: When the tractor drives into the house, first it's going slow, then travelling at nearly cruising speed.
Deliberate mistake: When the Gremlins take the tractor, from inside, the plastic around the cab is clear for visibility, but seen from outside, it's all black or opaque to hide the stunt driver.
Revealing mistake: As the second Gremlin in the kitchen is flinging dishes, the control rods attached to the puppet's left arm is visible.
Other mistake: Rand demonstrates the supposedly new razor attachment on the Bathroom Buddy. However, it was already on the device in the beginning.
Continuity mistake: As Stripe bites at Pete, Pete jumps back. A second later, he jumps back again.
Continuity mistake: When Gizmo goes to Rand for protection, he's upright as Rand's hand comes around to comfort him. A second later, he's in a reclined position, with Rand scratching his stomach.
Continuity mistake: As Billy opens the box, Gizmo pops up and goes back down. When the angle changes, Gizmo is starting to go down again.
Revealing mistake: When Stripe is dying from the sunlight exposure, in some of the shots you can see his puppet strings (especially visible on Blu-Ray). (01:36:35 - 01:37:20)
Continuity mistake: Billy gets shot with a crossbow bolt by Stripe and you see it in his left arm. Next shot cuts to a silver stereo/boombox, and then the shot cuts back to Billy. The crossbow bolt in his arm is now missing, but returns in subsequent shots.
Continuity mistake: Amount of snow on Katie's hair increases / decreases between shots after drunken Murray exits his car.
Deliberate mistake: When in the bar, or playing with the chainsaw, all objects swap from their real size to really tiny and perfect for Gremlins to grab.
Continuity mistake: When Dr. Hanson dismisses his students, a box falls, produces smoke, and he moves backwards. From a different angle the smoke is gone and he is repeating all the movements. (00:46:05)
Continuity mistake: Before Mrs. Deagle is attacked a portrait appears on her table between shots. (01:08:25)
Continuity mistake: When Billy's mom grinds the Gremlin in the food processor, the fridge to the left swaps from dirty to clean. (00:54:35)