Continuity mistake: Soon after the Gremlins hatch from their cocoons, Billy goes to the school to check on the professor. When he walks into the classroom, he leaves the door open. Later, when he leaves the classroom, he has to open the door again. (00:49:20 - 00:50:30)
Factual error: For a movie supposedly set in late December in a Northern state, all of the deciduous trees still have leaves on them. The most obvious place to see this is in the opening scene, when Billy is trying to start his car in front of his house. (00:07:05)
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. (01:42:00)
Plot hole: The whole film is basically told as a flashback from Rand Peltzer's point of view. Now he might be able to talk about things that Billy, his mom, or Kate might have told him, but he wouldn't have known about all the other the gremlins did to the rest of the town like killing Mrs. Deagle, the cops, or the gremlin in the mailbox.
Visible crew/equipment: Before Billy's mum pushes the gremlin into the microwave, you can see the top of a crew member's head, on the left of the gremlin, next to the microwave.
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. (00:14:10)