In the scene where Sigerson Holmes is eating the chocolates from the floor, he gets chocolate all over his face. Through the scene, the chocolate smudges on his face change. First it's very heavy, then its nearly gone and very light, and then when the camera angle is panned out the smudges are heavier.
When Orville is reading the paper, the section Sigerson hacks out falls away from him. In the next shot not only has the shape of the hole changed, but the paper is now folded inward toward Orville.
After his "duel" with the fencing machine, Sigerson is seen putting his street clothes back on. He starts putting on his pants...then repeats the action in the next shot.
The reflections of Orville and Sigerson in the mirror after they discover they have naked backsides don't match the actors' movements.
When Sigerson Holmes (Gene Wilder) and Sergeant Sacker (Marty Feldman) try to avoid the buzz saw in the narrow hallway, the back side of their pants should have fallen behind them as the saw went by. However when they made their exit, the scraps of their garments were up against the wall of the enclosure they were facing.
During Sigerson's duel with Moriarty, the clock behind Moriarty strikes eleven, distracting him. However, the clock only chimes four times.
While Holmes and Watson (in disguise) are serenading Sigerson near the climactic scene, the bow of Sherlock's violin is screwed too tight, making the wood of the bow convex. Although nowadays early music specialists do use this convention in imitation of baroque players, in Holmes' time it would be the sign of an amateur, inexperienced violinist.
At one point in the movie, one sees an advertising for OXO, however, the trademark was not introduced until 1899, 8 years after the setting of the movie.
The opening caption says the year is 1891. However, the calendar on the safe in Gambetti's dressing room, around 1:00:55, shows Wednesday, April 14, which day of the week and day of the month did not coincide between 1886 and 1897. But, since this is a fictional story, it doesn't matter.