How is this a film about the experience of film-viewing? What differentiates the film-within-the-film (Buster's dream) from the surrounding plot? What do the movements between film space and the space of 'real life' tell us about the nature of cinema?
What kind of fantasy of the self is involved in the projection into film pace? How does the Buster of the film-within-the-film differ from the Buster in the framing narrative? Why is he a detective in his fantasy, and how actually effective are his detective skills?
Why and how is Buster Keaton funny? How does he set up his gags and jokes? What mechanisms are involved? What uses of time and space? What does he do with his body (since most of this is quite definitely physical comedy)? What about his facial expressions (or lack thereof?)
Remember that this is a silent film. How are action, humor, ideas, and emotions communicated mostly without the use of words?