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.
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.
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.
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.
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)
Continuity mistake: In Dr. Hanson's lab, the model brain on the table changes positions between shots.
Continuity mistake: Billy opens the Gremlin's cage and leans forward to look at it. A frame later he is standing away from the box.
Continuity mistake: After Pete meets Gizmo, Billy grabs Gizmo by his head. A frame later he grabs him by his tummy.
Continuity mistake: Before the Gremlins attack the old lady, Gizmo is in the police office with a green string over his head. The string keeps changing positions between angles.
Continuity mistake: While Mrs. Deagle complaints at Billy for the broken snowman, her head is first to the left of the snowman, then to the right, without her having moved.
Continuity mistake: While Billy is trying to start his car, the wide shots show the door totally covered in snow, but in the close-ups there are uncovered parts.
Continuity mistake: When the movie ends, the sling around Billy's neck is either over the collar or under, depending on the shot. (01:38:35)
Answer: The original film was released before the PG-13 rating existed (it was one of the films responsible for its creation). Producers decided to remove some of the language and violence for the DVD release to avoid complaints about the PG rating.