The comments about Jonathan looking like Boris Karloff in the play—Boris Karloff originated the role on the stage. In fact, the only reason Karloff didn't play the role in the film was that he couldn't get out of his contract playing that role in the Broadway production. The producers of the play were worried ticket sales would drop if they lost their big-name star, even for a short time.
In the movie, Mortimer leans against a tombstone with the name "Archibald Leach" (Cary Grant's real name).
The casting of Peter Lorre as a crazed German surgeon may be a callback to Mad Love.
Casting Gag: Usually invoked with some of the larger productions; aside from Karloff playing a character that just happened to look quite a bit like himself, Bela Lugosi took over the role of Jonathan when Karloff went back to Universal, the subtext now that he'd been altered to resemble Dracula. Fred Gwynne took the part in the 1969 TV movie, and for the 1987 national tour, Jonathan Frid replaced Abe Vigoda (who also looked uncannily like Boris in the right makeup).
Money, Dear Boy: Inverted— Cary Grant was so dissatisfied with his performance in this movie that he donated his entire salary from it to charity rather than profit from it at all. This was not the first time, either — in 1940, he donated his entire salary from The Philadelphia Story to the British war effort. For this film he donated it to the American effort.
Playing Against Type: Cary Grant, who usually plays suave and sophisticated characters, in the movie plays a character who starts out like that, but becomes increasingly panicked and flustered as the story goes on.
Director Frank Capra is best known for uplifting, romantic, yet intelligent films. Here he directs a Black Comedy about a family of psychopaths.