Revealing mistake: When the thief places The Blue Carbuncle in the goose's throat, it's obvious he actually doesn't put the gem in the bird's mouth. He pretends to, but then drops the gem into his other hand. This is all visible in the shot.
Revealing mistake: When Holmes and Moriarty fall from the cliff, the wires holding the stunt men are plainly visible. Once they are falling in front of the falls, the wires are obscured, but when they are falling in front of the rocks the wires are easy to see. (00:48:19 - 00:48:48)