Continuity mistake: When Billy discovers Barney the dog wrapped up and hanging by the Christmas lights, Barney's face is pointed towards the house, but when the shot changes to Billy helping Barney down, the dog's face is turned away from the house.
Continuity mistake: When the gremlins are attacking Billy's mom in the kitchen, the kitchen is well lit with a window that allows sunlight into the room, but when Billy arrives at the house it's suddenly night time.
Continuity mistake: The first night in Billy's room, Gizmo is half a meter away from the Santa Claus hat, but when the angle changes he is just a couple centimeters away.
Continuity mistake: When Mrs. Deagle is killed by the gremlins, throughout the scene she appears to be either bare legged or wearing beige-colored tights. However, when her corpse is on the ground after being launched out of the house, suddenly she's wearing dark blue tights.
Continuity mistake: One of the mutated Gremlins scratches Billy's hand and then grabs an apple. On the desk there is a fake brain. In between shots it goes from being on its side to sitting flat.
Continuity mistake: When Billy is teaching music to Gizmo and the dog is laying on the bed, the wrinkle on the blanket next to the dog disappears between shots.
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: Both the scene of Billy, Pete, and the science teacher looking at the gremlin cocoon, and later when Pete is in class watching the science film, occur on the same day, yet Pete is wearing different clothes.
Continuity mistake: Amount of snow on Katie's hair increases / decreases between shots after drunken Murray exits his car.
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.
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.