Continuity: Holmes grabs a lamp off of the wall and puts it down by the hole in the floor. A short while later the lamp is back on the wall, but a short while after that it's back on the floor in time for Watson to trip over it.
Anachronisms: The postcard from Lesley has a picture of the Eiffel Tower occupying one entire side. Postcards of this type did not exist anywhere until 1901 or 1902, and in France not until 1904.
Continuity: When "Holmes" returns home after Watson's apparent death, the shadow of the house number on the inside wall, and other shadows, indicate strong sunlight from a certain angle. He then goes outside and the doorway is not lit that way at all. Also, the width of the panes around the house number doesn't match the shadow.
Continuity: When Sherlock Holmes is looking at Leslie Giles undressing, he makes a sound when she removes one stocking. Without removing the other she stands up and opens the door to check if someone's there. When she opens the door, both stockings are removed.