Revealing mistake: In the scene with the malfunctioning juicer, you can see the actor who plays Billy is about to laugh right before all the juice explodes out of the machine. As that is happening, you can see he has broken out into a full laugh. True, he might be showing some mirth over another one of his father's malfunctioning inventions, but he was about to break out into laughter before anything happens, and his laughter is inconsistent with his frustrated demeanor when Pete walks into the kitchen.
Revealing mistake: Just after the mum liquidises a Gremlin, she then has to deal with one throwing plates. If you look carefully, whenever the plates are thrown from the Gremlins perspective, whenever its left arm comes into shot, you can see the puppeteer's rod used to move it.