The clue about the double space after a period was not entirely correct. While a text message would retain the double spaces, a word processor might not. Many word processors automatically change the two spaces to one by default, but this function can be overridden.
The scheme to overdose someone with morphine would not have worked. Morphine pumps are programmed to not dispense more than what the Doctor prescribed. It therefore wouldn't have mattered how many times the button was pushed, at most it would have put the patient to sleep.
At the very beginning of the episode, two face-to-face women whisper dialogue to each other on stage rather than use a "stage whisper," so it would not have been possible for anyone in the audience to hear anything they said.
A police officer in full uniform would *not* bring food or drink past the crime scene tape, nor would an officer in uniform wear a non-regulation (plaid) scarf, otherwise that officer would face disciplinary charges for violation of the uniform dress code.
Elsbeth gushes to Professor Modarian that she wants to see "Cats" while in New York. The original production closed in 2000, while a revival closed in 2017 and there has been no NY production since. Though Prof. Modarian does indeed question if there's another revival, so this may be intentional to demonstrate how much Elsbeth is an outsider and not a knowledgeable New Yorker.