Revealing mistake: In the scene where Chitty is taking off from the castle, Caracticus looks down at the toymaker and Peter and says, "Bye bye". If you look closely, right in front of them, a boy runs across holding a stick he stole from one of the cavalrymen. He is waving it around and you can tell it's fake because it flops around like rubber.
Revealing mistake: During the "Toot Sweets" number in the factory, the cart with the candy trays move freely, however later on when they start spinning on them in circles (right after Jeremy gives Mr. Scrumptious another sweet) you can see each one is spinning due to a pole holding it. You can see it just under the bottom trays.
Revealing mistake: During the "Grow the Roses" number, there are several shots of the wheels of the Baronial car, looking normal. In the final shot of the scene (when the car falls apart) square supports disappearing into the floor have suddenly appeared on the axles, as part of the mechanism to support the car when the wheels fall off.