Batman and Robin may not have been aware that the guy with the gun is the real Skid Turkel until he announced it, but they sure do now, on the cover of Batman 74 (Dec/Jan 52/53).
The Joker’s sanity is central to the Schwartz, Sprang and Paris story that opens this issue.
The Joker pulls a series of childish and pointless robberies at the top of the story, clearly trying to establish that he has gone insane. Batman figures out that the Joker has a reason for wanting to be sent to an asylum, and so, in disguise, gets sent there as well. Though an asylum is shown, there is nothing to associate this clean and modern facility as Arkham Asylum.
Batman quickly gets the Joker’s plan, to learn the secret hiding place of the loot of one of the inmates. He tries to help the scam along, but in fact just gives himself away. The Joker straps Batman into a straightjacket, tosses him into a sealed room and begins to flood it.
The climax of the tale gets quite funny, as Batman and Robin play games with the Joker, with the help of an inmate who believes that he is Batman. By the end, the Joker seems to really have gone crazy trying to figure it all out.
Finger and Sprang give Alfred an acting role in this story, as he is considered the double of Skid Turkel, an imprisoned enemy of Batman, and the subject of a movie.
Alfred has to shave his moustache and wear a skin head cap to play the role. We see the back story on Turkel through the shooting of the film, which makes this a more interesting read than usual.
The cover provides the plot twist, as Turkel escapes, grabs Alfred and uses the film shoot to try to kill Batman. But Batman had already figured out that Turkel was not Alfred, by his necktie.