Factual error: Water causes Gremlins to multiply. But in a shot during a cooking show, the insane Gremlin (Daffy) pops up in a pot of soup, which is water based, yet he still doesn't multiply.
Suggested correction: There have been other times when mogwais and gremlins get wet and don't multiply suggesting it's water, not water based liquids. In the first movie for example when the gremlins are drinking beer and Gizmo gets licked by the dog without multiplying.
Character mistake: Given Billy still remembered and recognized him it seems strange Kate doesn't when she mistakes Daffy for Gizmo.
Suggested correction: Billy spent significantly more time bonding with Gizmo in the first movie - days and days. By contrast Kate had very little actual time with him.