Plot hole: When Holmes starts the human chess game, he says, 'Who had entered the lists, the king's pale knight.' This refers to moving the white knight of the king's side. However, the ritual does not mention to which square it should move. Still having three possible squares to move to (since the knight is on its initial square and the game has already started), Holmes knows and indicates that the knight (Dr. Sexton) must move to square F3.
Factual error: In the scenes set during 1918, Clive is shown wearing a typical late 1930s/WW2 military production British steel helmet with its distinctive canvas covered sprung chinstrap.
Revealing mistake: When the mice are feeding the cat, the cat sits up and a mouse passes through his head.
Continuity mistake: When Jerry launches his egg carton, there are initially three light bulbs in the back, but when he releases the bulbs, there are now four.
Continuity mistake: When Droopy is standing the door, he tells the convict he's going to call the cops. At this point you can see there is nothing next to Droopy on the frame, but in the very next shot a hinge has appeared.