Chuckie's pet bug dies and Phil and Lil's goldfish is implied to have died in the past. The twins are also said to have once had turtles but not anymore, although it's unknown what happened to them. A spider also dies in "Spike Runs Away". But if you avoid "Spike Runs Away", "I Remember Melville", and "Autumn Leaves", you can be assured that there are probably no animal deaths.
Tommy is kidnapped by some crooks who mistake him for a wealthy family's child. Not helped by the fact that it's one of the early episodes where the babies don't speak at all so it's frighteningly realistic on top of that
In "Chuckie vs. the Potty", Chuckie wets his pants twice and Angelica wets the bed, in "Accidents Happen" Chuckie wets the bed, and in "Officer Chuckie" Angelica berates Chuckie for wetting his pants.
One episode is about Angelica trying to take a tooth out of Chuckie's mouth so that the tooth fairy will collect it. She fails, but knocks out one of her own teeth.
There was one episode where Charlotte thought she was pregnant and then she wasn't. She *might* have miscarried then, but I'm gonna put "no" since she probably just botched the pregnancy test.