The play that Murdoch and Dr. Ogden are seen leaving is "The Importance of Being Ernest" by Oscar Wilde. It premiered in Great Britain in 1895.
The development of the magnetron, which eventually made the microwave possible, goes back to the early 20th Century. The microwave goes back to World War II and was patented in 1945.
The weapon featured in this case is a heat ray, and closely resembles the weapon used by the Martians in H G Wells' The War Of The Worlds, which was first published in 1897. Martians were also featured in the series 1 finale.
In a homage to Alfred Hitchcock's film North by Northwest (1959), Murdoch says that the triangulation signal is coming from the direction of "north by northwest."
This episode takes place in September 1897.