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. (01:27:55)
Revealing mistake: When Flint screws the fuse into the fuse box to get the lights back on his dad just appears out of thin air.