The dog who jumps on Niles' lap is actually Enzo, the son of Moose who normally plays Eddie. In Niles' apartment, it's again Moose playing Eddie. This is the start of Moose and Enzo sharing the role of Eddie due to Moose's aging and tiring easily. Eventually, Enzo takes over the role permanently.
The title is a reference to an Alfred Hitchcock film Dial M for Murder (1954). Furthermore, the name of Frasier's love interest, Rebecca, is also the title of another Hitchcock film.