Continuity mistake: In the title sequence a Rube Goldberg machine can be seen. The error can be seen by watching the four revolvers rotating and then a single revolver firing. When you look at all four revolvers, there are hand grips in each one, but in the closeup shot of one actually firing, the hand grip is empty. You can't see it later than S5E18 because they decided to delete the frames when you can see all four revolvers, and left only closeups.
Continuity mistake: When Holmes and Watson are arguing in the kitchen, Watson puts her mug and phone on the counter. A few times during the scene, the mug switches which side of the phone it's on. The first time it's plausible Watson moves it when off camera, but subsequent to that, we can see enough of Watson to tell she doesn't make enough movements to change the position of the mug.