Revealing mistake: When the professor is trying to find the gremlin, he is in the room with the movie playing. The projector that is playing the movie is actually moving backwards. (00:44:35 - 00:47:35)
Revealing mistake: Billy is on the floor about to get attacked by Stripe. You can see the rip in Billy's jumper before Stripe has scratched him. (01:00:30)
Revealing mistake: When Mrs. Deagle is visited by Christmas caroling gremlins and one hot wires her chair, as she shoots up the chair, she passes the same pictures on the wall at least four times. (01:09:30)
Revealing mistake: Not long into the film when Billy wakes up to find the dog tied up in Christmas lights it's obviously a fake dog, when the camera view is onto the front of the house. (00:29:05)
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.
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.
Revealing mistake: As the second Gremlin in the kitchen is flinging dishes, the control rods attached to the puppet's left arm is visible.
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)
Revealing mistake: In the scene with the malfunctioning juicer, you can see the actor who plays Billy is about to laugh right before all the juice explodes out of the machine. As that is happening, you can see he has broken out into a full laugh. True, he might be showing some mirth over another one of his father's malfunctioning inventions, but he was about to break out into laughter before anything happens, and his laughter is inconsistent with his frustrated demeanor when Pete walks into the kitchen. (00:22:40)
Revealing mistake: Gizmo flies off a snow shovel on his car and it blows up. There is a noticeable edit here where the effect happens. It's likely the car didn't blow on the first take so they spliced two scenes together.
Revealing mistake: When a Gremlin shoots Kate, the glass is already shattered before the bullet hits it. (01:17:15)