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.
Although very beautiful, the gowns worn by Truly Scrumptious are outdated for the time the film is set.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.
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.
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.
When Grandpa Potts first arrives in Vulgaria, he says, "On behalf of Her Majesty, the Queen..." but in 1910, the reigning monarch was King Edward VII, or George V who took the throne after Edward's death that same year.
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.
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.
When the spies try catching Chitty under a bridge, Mr. Scrumptious's car drives through their picture of the tunnel and into their truck, but as his car breaks through the picture, you can see briefly that there's nothing behind it. No truck. In the next cut they go right up the ramp and into the truck.
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.
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.
During the Baron's birthday party, Truly (as a doll) dances atop a music box spindle within an unfolded screen of mirrors, visible on the floor for all the guests to see. When Caractacus (as a puppet) rises from his box and starts to dance, the camera pulls back; Truly's music box is nowhere to be seen. When Caractacus goes over to sing a duet with Truly, suddenly she and her music box are visible again.
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, the children and Truly are driving in the water at the beach getting away from the Baron's ship, the same mountain is seen passing by two or three times.
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 sing and dance before attending the birthday party, the Baroness wears high-heeled shoes, but when she falls through the trapdoor, she wears flat shoes. When she shortly re-appears, she again has on high heels.
When Edison the dog breaks free of his leash during "Toot Sweets", he knocks the pedal bike over and drags it across to the steps. Two shots later, when the horde of dogs runs toward the factory, they run up the steps where the bike is seen standing neatly upright as before.
When Chitty switches to "boat" mode after the tide comes in, you can see a stick or rod lifting up the propeller in the back. This rod is not present in any other shot where the propeller would be visible.
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 the 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 reappears upon landing at the castle.
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.
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.
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.
When we see Chitty in the scrapyard, the front wheel (and probably axle) is clearly damaged making it not roadworthy yet when Potts brings it home, it is apparently undamaged and running quite freely on a tow.
When the Baroness ejects from the car, the Baron shoots her down. As the Baroness falls into the lake, we can see the lake disturbed in a circular pattern from the downdraft of a helicopter just before she hits the water.
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.
The cooking machine heats plates hot enough to fry eggs and sausages before sending them down the ramp to the table. When the plates and metal roller frames arrive at the table, they should still be hot enough to cause burns; however, Mr Potts and the children grab the "burning hot" plates with their bare hands.
After Truly brings the children home, their father tells them to go inside for tea. It is probably mid afternoon, i.e., no sign that the sun would be setting soon, but by the time they finish eating a bit later, their father tells the children to go up to bed as it has become dark. There was not enough time between them returning home and eating for it to be bed time and dark out.
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.
During the close ups of the Baron and his officers on the bridge of his yacht, at the chase of the boar motorcar, the funnels behind them have small wrinkles on them, revealing they are set pieces covered in some sort of metal foil, instead of the solid, brass-looking funnels visible in the wide shots.
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 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 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, but 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.