In the beginning of Shutter Island, when Teddy and Chuck are about to enter Ashcliffe, there is a female patient in the garden that signals a shush to Teddy. What is the significance of this gesture?
As the movie reveals that it is a planned experimentation on Teddy to bring back his memory, I assumed that Teddy was a patient of that place, that the lady knows Teddy and what he had done. As everyone was present there she could not directly talk to Teddy and say what she wants to say. She was just trying to convey a message to him with that gesture: Do not fall in their trap, you have done things. However this was my take on the scene.
The creepy old lady does the shush sign to Teddy because the doctors had told everyone in the hospital about the experiment they are conducting with Teddy, and that they are not supposed to say anything to him about it. The lady is mentally ill and she was telling Teddy to be quiet, in essence not to spoil the secret.