Continuity mistake: When Bill is in the bar drawing a cartoon of Mrs Deagle, the amount of popcorn on the table increases between shots.
Continuity mistake: After Gizmo poops, there's a close-up on Billy's stunned face, perfectly lit. A frame later, from a different angle, the face is in shadows.
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.
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.