During the Big Ben sequence, Ratigan's necktie comes off at one point, but then it's back on when he and Basil fall down the clock tower, and then disappears when they land on the clock hand.
When Dr. Dawson and Olivia are seeking Basil's help at his house, Basil slouches down in his chair and starts playing the violin, holding it in his right hand and having the bow in his left. When Basil sits up in another shot, he is holding the violin in his left hand (like it's supposed to be) and the bow in his right.
During the mousetrap scene, Hiram Flaversham (Olivia's father) is tied and gagged. When we cut back to him again from another shot of something else, the gag is missing.
Fidget's peg-leg is normally on his right-hand side, but when Olivia stomps on his toes, his peg-leg is on his left-hand side.
After escaping Ratigan's trap, Basil changes from his sailor disguise to his regular clothes. When he's done, he is clearly wearing the blue sailor pants under his coat. When posing for the camera, however, he is wearing his regular brown pants.
Basil deduces that Rattigan's lair must be adjacent to the Thames because of traces of salt water in Fidget's list. However, the Thames is not salty when it flows through London.
In the beginning, Basil shoots a bullet to compare the ballistic fingerprints of each bullet. He then lines the two bullets aft end to aft end and compares the scratches to verify his lead. This will result in incorrect results because if you rotate a bullet 180 degrees, the scratches will become mirrored and two matching bullets will not align.
Toby doesn't have any nostrils.
At the toy store, in order to do checkmate on the chessboard, Basil would have to move the rook to the h4 square, which is on the edge of the board.
However, the square he moved the rook to is clearly somewhere in the middle of the board, as it is surrounded by other squares in all directions.
Although Disney's Dumbo (1941) wasn't released until 1941 and the film is set in 1897, the elephant bubble blower seen the toy shop is simply an elephant that happens to look like what Dumbo will. This is merely an easter egg for Disney fans. It is not meant to be a toy replica of Dumbo.
Shots of Basil handling Fidget's list show no writing on either side of the paper.
In the opening shot of the Big Ben sequence, there is a cog just to Basil's left whose teeth go through a staff next to it.
The "Let Me Be Good To You" number has a clarinet as part of the arrangement. Yet no clarinet player can be seen in the band.
After Basil tells Toby "To Buckingham Palace!", as Toby begins to run at the next shot, a black vertical line suddenly appears.
Basil and Dawson are being put in the trap, right when Ratigan removes his hand and says "Thus ends the short and undistinguished career of Basil of Baker Street", one of his cuffs turns white, and then gold again.
Dawson claims to have just gotten back from Afghanistan. The film is set in 1897.
The Second Anglo-Afghan war was fought from 1878 through 1880. The war ended 17 years before the events of the film. There was a third Anglo-Afghan war but it was fought in 1919, 22 years after the events of the film.
In the film Professor Ratigan smokes a cigarette with a modern day cigarette holder. The film is set in 1897. Modern day cigarette holders were not invented until 1910 and did not become fashionable to use until the 1920s.
Basil is seen smoking a cigarette in the seedy bar. Ratigan is seen smoking a cigarette using a cigarette holder. The film is sent in June of 1897. Although cigarettes were around in 1897 they were expensive and all hand rolled then, usually in either Egypt or Turkey. They would've been too expensive for low life criminals back then. Pipes and cigars were more common among the populace then. It wasn't until the 20th Century and the invention of automated cigarette-making machines that cigarettes became more popular.
When Basil and Dr. Dawson are in the mousetrap in Ratigan's lair there is a phonograph record as part of the contraption. The film is sent in June of 1897. Although Thomas Edison invented the phonograph in 1877, it did not become available for home use in the USA until 1896 and in Britain until around 1900. Around three years after the events of the film.
In Ratigan's lair his henchman are drinking champagne from modern day champagne flutes. In 1897 the champagne coupe glass was what champagne was drank from. The flute did not become popular until the 20th century.
During the climactic fight, as Ratigan says, "There's no escaping this time, Basil", his lips don't match the dialog.
Right after Basil jumps onto the tail of Ratigan's aircraft, the propellers are not moving, yet they can still be heard.
221 Baker Street is portrayed as a large detached house. In reality, it is a townhouse.
At the end when Flaversham checks his watch and tells Olivia to catch their train and for her to come along it remains unknown if they were going back to live in the toy shop or if they were going to move away from London.
When Ratigan talks to Hiram when he is near the bottle, we see Olivia in the bottle, wearing her Tam O'Shanter hat. But Fidget wore it earlier (along with Olivia's scarf and dress), and we don't see Olivia's clothing after that until the final scene so Olivia couldn't have gotten her clothes back just yet.
Fidget somehow finds Olivia at Basil's apartment, yet it's evident that Ratigan did not instruct him to go there. The arch-villain was surprised when Fidget told him he ran into Basil at the toy shop, and obviously didn't realize that Basil was already working on this particular case.