Potts is supposedly inventing the first vacuum-cleaner in 1910. The gag fails because the first vacuum-cleaner was already invented in the 1860s and the first electric vacuum-cleaner was invented a few years before 1910.
The locomotive overtaken by Chitty Chitty Bang Bang in the main song sequence is a J94 "Austerity" Saddle Tank locomotive. It has the legend "GWR" (Great Western Railway) on the side. The J94 type of engine was not built until the 1940s, and no J94s were ever operated by the Great Western Railway. Also, the GWR livery was a deep green, not blue as shown.
In the opening sequence, the 4 races seen are the "1907 British Grand Prix", the "1908 French Grand Prix", the "1908 German Grand Prix" and the "1909 British Grand Prix". However, there were no British or German Grand Prix until 1926, in Germany the precursor to the Grand Prix was called the "Prinz-Heinrich-Fahrt" in 1908.
Although very beautiful, the gowns worn by Truly Scrumptious are outdated for the time the film is set. If the car was retired in 1909, the film would at least be set in 1910 or later. Truly's outfits were quite stylish from about 1897-1907, but fashion began to change after that, and if she were as rich as she appears to be, would have worn fashions more up-to-date.
Although characters refer to the airship seen in the film as a "zeppelin" strictly speaking it is not. A zeppelin is vehicle with a rigid framework that contains multiple gas cells used to lift the craft into the air. Passenger compartments and mechanical areas are usually within the framework as well. The aircraft seen in the film would be classified as a (semi-rigid) airship.
During the scene where they take Chitty out for the first time, Grandpa states that he is going to Alaska (statehood established in 1959, movie made in 1968), unfortunately it was referred to as the District of Alaska or the Alaska Territory at that time. Not necessarily inaccurate, but an interesting statement.
During the birthday party for the Baron, Musicbox dances on a spindle within an opened large box of mirrors. This box is visible on the floor for all the guests to see. When Ragdoll rises from a box, he starts to dance, the camera pulls back and Musicbox is nowhere to be seen. When Ragdoll goes over to sing his duet with her, suddenly Musicbox is visible again.
When Edison the dog breaks free of his leash during "Toot Sweets", he drags the push bike over and across to the steps. Two shots later, when the bunch of dogs are running towards the factory, running up the steps and the bike is neatly upright as before.
At the end of the seaside picnic, before Caractacus begins telling the pirate story, Truly ties the picnic basket onto the back of the car. The basket is absent as the car cruises on the water, but reappears when they drive out.
When the first Chitty crashes, the front end suspension is badly damaged and the left front wheel is bent. However, when the car arrives at the Potts workshop, the front end is not damaged and the steering works fine.
When Truly joins the Potts' on their picnic, she is wearing her leghorn hat with the scarf tied over it. Both times the family leaves the beach (in the story and after the picnic), she has her scarf but the hat is nowhere to be seen.
When Mr Potts pushes Chitty Chitty Bang Bang out of his workshop, the tires become coated with sand and dirt from the dirt driveway. In the next shot, the car is in the same place, but the tires are clean.
In the interior shots of the car when the Professor, Children and Truly are driving in the water at the beach, running away from the Baron's ship, the same mountain is viewed passing by two or three times.
When the spies are trying to catch the car under the bridge Mr. Scrupmtious crashes through their picture of the tunnel and into the truck but as the car goes through the picture you can see briefly that there isn't anything behind it. In the next cut they go right up the ramp and into the truck.
During the shots of the haircut and the man chasing Mr Potts, we see a carousel operating in the background. It is running at full speed during most of the shots. In one shot, it is slowing to a stop. However, about 15 seconds later, we see it at full speed again.
As the family are preparing the table for dinner, Mr Potts casts the tablecloth over the table, covering the children. In the next shot, camera positioned under the cloth, the children are standing right next to each other. When Mr Potts takes the cloth off, they are standing at least two feet away from each other.
The two spies carry a painting of the bridge and tunnel, wrapped onto a pole about half the length of the tunnel's upper wall. As it drops over the edge, the film jumps due to a cut. The pole suddenly spans the entire length of the wall.
At the end of the Toot Sweets song Lord Scrumptious is on the right side of the camera near his daughter. But when they cut back to him a second later to make the last note he is on the left side of camera alone.
During the POSH song, Grandpa drops his pith helmet as the privy jerks downwards and is nowhere in sight for the remainder of the scene, presumably dropping into the sea. However, it has reappeared upon landing at the castle.
When Chitty Chitty Bang Bang is on the sand bar and Caractacus Potts begins telling his story, the girl Jemima Potts is holding a half-eaten apple. After the boat appears and heads towards them, Jemima is holding a much-less eaten apple, with only a few bites out of it.
When the Baron and Baroness are singing and dancing before the birthday party, the Baroness is wearing high-heeled shoes, when she falls through the trapdoor she is wearing flat shoes and when she re-appears she is wearing high heels again.
In the last shot of the still-closed barn doors, just before the cut to the children at the window with Jemima saying "It's awfully quiet in there!", the barn door on the left can be seen beginning to open for a split second.
When the Baroness was ejected from the car and the Baron is shooting her down, as the Baroness is falling into the lake we can see the lake disturbed in a circular pattern just before she hits the water. This looks like the downdraft of a helicopter.
In the seaside picnic scenes, the overhead shot of Chitty Chitty Bang Bang arriving at the beach and leaving the beach show an underwater ramp on the right side (used for when the car was in the water). This is also visible during one of the other beach scenes.
The owner of the junkyard tells the children that their father must come and buy the car before tomorrow morning when the other man will come to pick it up. Potts actually misses this deadline by one day. Counting the nights in the movie, the children go to sleep twice before Potts buys the car.
When Chitty comes in to rescue the Potts and Miss Scrumptious, she (Chitty) makes a turn on the floor. The car is clearly turning tighter than the front wheels will allow, it is on a dolly of some kind.
The cooking machine heats the plates hot enough to fry the eggs and sausages and then sends them down the ramp to the table. When the plates and metal roller frames arrive at the table, they would still be hot enough to cause burns. However, Mr Potts and the children grab the "burning hot" plates with their bare hands.
In the opening sequence, during the French Grand Prix, car 42 is seen losing a wheel on a turn, followed by car 2A. There is an obvious jump in the editing where they combined the first shot of car 42 losing its wheel and the second shot of where it's been placed.
The goof items below may give away important plot points.
At the end of the movie, Grandpa introduces Lord Scrumptious as "my Brigadier" about whom he has been telling stories all Caractacus' life. It's not likely that Lord Scrumptious would have changed his name since the time when Grandpa was his batman, so it shouldn't be a surprise to Grandpa that "His Brigadier" had lived nearby all this time.
When we see Lord Scrumptious's car at the end of the movie, Potts has pulled up behind him, and both are facing the house. When we see Chitty flying around the house, Lord Scrumptious's car is inexplicably turned the other way.
When the King's guards storm the main doors during the big fight, some boys throw several buckets of liquid on the stone to make the soldiers fall. A few seconds later there is a shot of more soldiers running in and the stone is clean. In the following shot the mess is back again.
The imprisoned children attack the upper-class people in the castle. Someone pours liquid from a goblet down a woman's front. On the base of the goblet, there is a code shown clearly. The code is 696 A.