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.
Revealing mistake: When the Vulgarian boat is chasing Chitty in the sea, Truly, Jeremy and Jemima are obviously dummies in the far shots because you can see them flopping about in the car.
Revealing mistake: In the baron's birthday party scene Mr. Potts is dressed in a rag doll costume. In some shots, you can see the wire that holds him up when he jumps.
Other mistake: In the scene where everyone is going to get away from Vulgaria in the car, Grandpa scrambles in after them. You can distinctly see a Vulgarian soldier give him a shove to get him in the car, then do his "Run away." thing.
Continuity mistake: When the car which becomes Chitty crashes in the beginning, the vent and the front left wheel become totally loose, but in the next scene where the children are playing in it, the vent and the wheel are attached.
Continuity mistake: When Jeremy and Jemima tell Mr Potts about the car at Mr Coggins' place and how Coggins told them they could have if Mr Potts paid him 30 shillings, they tell him to give Coggins the money in the morning, presumably so the junk man can't take the car. However, the next morning, they all instead go off to the sweet factory to show Mr Scrumptious the toot sweets Mr Potts discovered the night before, and it's actually not until the day after (after Mr Potts got all that money at the funfair during the night) that Potts finally pays Coggins and gets the car.
Revealing mistake: In the scene on the beach between Truly and the children, waves are seen lapping against the sand castle but not washing it away - it's made from something more substantial than compacted sand.
Continuity mistake: In the scene where all 4 characters are first riding in Chitty (waving at the train and just after), the two children riding in the back seat alternate between wearing hats and not wearing hats. This may have been done to conceal actor's doubles.
Continuity mistake: In the "Chitty on the water" scene, when Chitty has deployed a float her wheels become horizontal. In the far way shots, the wheels aren't moving. In the close up shots done in the studio, the horizontal wheels are spinning and there is no visible raft beneath the boat.
Continuity mistake: When the two spies try to capture Chitty by parking their open van under the railway bridge, then dropping a canvas screen down over the top so it looks like the road under the bridge is clear, as Lord Scrumptious's car hits the screen and tears through it, you can see that there is nothing parked on the other side. The van is gone. Yet the following shot establishes the fact that the trap has worked successfully; the car has gone through the screen and ended up in the back of the van.
Continuity mistake: When they are almost done singing "You Two" there is a big ripple in the tablecloth. After they finish singing and the plates are rolling down, the ripple is gone.
Continuity mistake: During Mr Potts's solo dance as the rag doll, Truly as the doll, the music box and the surrounding mirrors completely disappear, and then reappear again ready for Mr Potts's and Truly's duet.
Continuity mistake: In the scene where Mr Potts is putting the children to bed they offer him the objects from their treasure chest: a ivory tusk, "jewels" and a "crown". Near the end of the song he puts the objects back into the box but not the crown.
Plot hole: Near the end of the movie, when Mr Potts finds out that he's going to be rich (Mr Scrumptious wants to buy his invention) and he rushes out to his car to go see Truly, he meets her en route and she's got her hair in an really elaborate style and has changed. But there is no way she could have possibly got to her house, found out that her father had gone to see Mr Potts to buy his invention, changed her outfit, done her hair like that and gone out to see Mr Potts in the short amount of time between Mr Potts and his children dropping her off, and Mr Potts and her meeting at the pond.
Character mistake: Before the junk man drives away he calls Mr Coggins "Bill." The correct first name is George.