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.
Although, Warren is stated to be from a different city and hadn't even heard of Arkham when he got sent there, so even if the jury accepted his plea for the reason stated above, in truth it was a case of severe stupidity on his part (and certainly the part of his lawyers, whose reactions to the judge's sentence shows they are fully aware of what Arkham entails, so really should have seen it coming).
Once you learn what Doodlebug's paint is made of, that scene from his prior escape, while initially little more than weird, becomes absolutely terrifying.
The original to the story inmates, they are not big name like Joker or Two Face but they are as horrifying. Death Rattle and Jane Doe are just examples of what a regular inmates is for Arkham Asylum, now think how many time there is a breakout in Arkham Asylum allowing murderers like them who don't have any fixation with fighting Batman to hold their mayhem.