Continuity mistake: Right after the mom sprays the Gremlin in the face with the flea and tick spray, forcing him into the microwave, we see the Gremlin cooking away in the microwave with the spray can in the foreground, its label facing the camera. In the shot where the Gremlin blows up, the can's label is no longer facing the camera, plus immediately after the Gremlin goes ka-blooie, something cracks in front of the spray can, distorting our view of it.
Continuity mistake: Watch Billy after he has been first attacked by Stripe by a clawing to Billy's chest. He is wearing a sweater with a white t-shirt underneath. From that moment on the torn area of his sweater and the blood marking on the white t-shirt continuely change shape and size. And if Stripes claws were sharp enough to cut him that bad then how come it didn't cut through his white t-shirt under his sweater. Because Billy showed alot of pain when he was clawed.
Continuity mistake: When the old man is leaving the family's home, in the indoors shot as he turns to walk out the front door, he is holding Gizmo's box under his right arm, and has the "smokeless ashtray" in his left hand. Cut to the outside shot of him walking through the door, and he is suddenly holding the Mogwai box by it's handle, and has nothing in his left hand.
Continuity mistake: This is in the scene near the beginning of the movie at the bar where Billy's girlfriend works. Billy is sitting at a table drawing. He is joined by the Vice President of the bank he works at. He sits down and starts talking to Billy. Billy looks up at him while he's talking. Then in the next shot, which shows them both, Billy is looking down at his drawing as if he weren't even paying attention.