Revealing mistake: In the scene out West with the buffalo, notice the car driving in the distant background.
Factual error: The movie takes place in the early 20th century (1910s or 1920s or so). When Dean and Jerry are riding in a RR cattle car with its doors open you can clearly see parked automobiles from the 1950s through the open door of the train car.
Continuity mistake: When Frankie punches Barakov, pushing him through the window, not only do you see the wires lifting him, but it is obvious that the inside of the building is a studio set as not only does the window get broken, but also the wall above it is torn. The wall is obviously made of paper and the scenery outside the building is a painted backdrop. And when the angle changes to outside the building, only the window is broken but the wall is intact.
Continuity mistake: When we see Dorlock Holmes at his desk at the start of the cartoon, you can see that he is writing with the feather in his right hand, but in the next shot he is holding the feather with his left hand.