scam: (first quotation 1963, origin unknown)
go missing: 1940s. For more on this, see this post: http://katherinebarber.blogspot.ca/2010/08/usage-issue-go-missing.html
cock-up: first quotation 1948
beauty salon: first quotation 1906, did not become part of general parlance until a decade or so later. "Beauty parlour" would have been the more common word in Murdoch's time.
Another usage that strikes me as an anachronism, but in the other direction, so to speak, is Murdoch's habit of always asking Constable Crabtree: "What have you?" The use of "do" to form questions arose in English in the Renaissance. Although Jane Austen was still using "What say you?" as a construction in the early 19th century, the "What do you have" construction would, I think, have been more idiomatic by the early 20th century. It's very difficult to verify this using online tools, however. The "what have you" pattern is now used almost exclusively with a complement, as in "What have you to say for yourself?" and to a certain degree in the fixed phrase "What have we here?"
For more Murdoch anachronisms, see this post and this one.
P.S. If you find the English language fascinating, you might enjoy regular updates about English usage and word origins from Wordlady. Receive every new post delivered right to your inbox! You can either:
use the subscribe window at the top of this pageOR
(if you are reading this on a mobile device): send me an email with the subject line SUBSCRIBE at email@example.com
Follow me on twitter: @thewordlady