During Dr. Carver's montage of speaking with Arkham inmates, the Riddler calls her "my deer girl." Typo? Or is Riddler aware that "Dr. Carver" is actually Jane DOE?
Issue four gives further evidence to Riddler knowing that Dr. Carver is actually Jane Doe, in the form of a riddle written with soapy water seen during the scene where Cash has Riddler pinned against the wall in the shower. It reads 'Who got out by getting ahead?'
Somewhat less subtly, practically all of Dr. Carver's narration and behavior in the first issue takes on a different meaning once you know it's really Jane Doe disguised as Carver.
Trying Insanity Defense in Gotham is insane, because if the jury buys it you are sent at Arkham with Joker and all the other monsters. That's why the jury accepted Warren's plea: he was clearly insane doing it there.