Revealing mistake: In the shot right before Coraline finds the hidden door for the first time, she says "Alright Little Me, where are you hiding?" and drops her notebook and pen on the floor. When the notebook and pen are falling, you can see the wires that were used to suspend them while they were being animated. It's a common stop motion technique, but these days they usually try to paint the wires out afterward. It's a pretty severe dutch angle though, and they're only visible for a few frames, so it's easy to miss.
Revealing mistake: When Coraline visits the other world a second time she sees the Other Mother moving cheese along a grater as the camera pans down. The second time she "slices" the cheese, various pieces stick to the end of the grater. The third time she runs the cheese along the grater, these pieces fall off along with the last piece. As the last piece falls, a wire can be seen that is used to suspend objects in the air for films like these. Additionally, one piece of cheese is stuck on the underside of the grater as the Other Mother taps it clean, but mysteriously disappears in a single frame when she lifts it up out of the way.
Revealing mistake: In the scene where Coraline is in the garden in the other world looking for the ghost eye, she looks through the magical seeing stone and spots the other father on his mechanical praying mantis tractor. When he arrives at the bridge, and it snaps, he breaks off the ghost eye from the gear stick and then he collapses through the bridge into the water. But if you look closely, he is slipping through what looks like some black material, not real water.