As Watson is looking through the Who's who reference book publications for an idea of who the illustrious client is. He picks the forth book along for the year 1902. In the next scene you can clearly see a gap showing the second book missing instead of the right one from the previous shot.
The Baron is seen cutting the corners of a photo and pasting it into his journal, but photographs only look cornerless in albums because of the mounts that hold them in place and which make pasting superfluous.
In one scene, Baron Gruner is listening to a recording of a baritone singing the "Madamina" aria from Mozart's "Don Giovanni", and the singer is backed by a full orchestra. Such recordings were impossible to make in the nineteenth century, when the story takes place. Until the advent of electrical recording (i.e., using microphones) in 1925, singers and instrumentalists had to stand around a large horn to make recordings, and the use of a large orchestra would have distorted the sound. Special "chamber music" arrangements had to be made of orchestral pieces to prevent distortion and overload. Recordings were made on wax cylinders then, not discs, and the quality of sound was far worse than demonstrated in this episode.
When the telegram boy brings the message,watch the railings move.