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.
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.
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: 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: 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.