When discussing the hidden code in the song, Professor Montague (actor Arthur Malet) stumbles over his lines and mispronounces the words: "We may find that there is a cryptogam/cryptogram within the code".
The talking machine that Pike finds in the music store is a device of the type that Thomas Edison finally devised in 1888; as such, its appearance here is some ten years too early. Edison's machine was hand cranked, recorded on tinfoil cylinders and were barely audible on playback. It did not have any type of sound amplification, so recordings were made by shouting loudly into the horn. The voice on the playback is in a normal speaking tone, making this a factual error as well.
In the first conference in Blessing's office, West is studying what appears to be a fingerprint card. Although finger and handprints have been used as identifying marks since ancient times, the formal study of fingerprints and their use as an identifying tool did not start until the later 19th century. The first papers on fingerprints as a means of identification appeared in the 1880s, and the first fingerprint bureau opened in Argentina in 1892. The first use of fingerprints in a US criminal case occurred in 1902, and the inclusion of fingerprints in criminal records began in New York in 1906. So it is unlikely that, in the 1870s, that even the Secret Service would have been keeping fingerprints on file.