According to Jessica Chastain, Annabel's octopus tattoo describes her character. When Annabel found herself caught in a situation she did not like, such as the octopus, she would take off her tentacles and grow new tentacles to escape.
When Annabelle Is watching TV (about 41 minutes Into the Movie) she looks at the screen and says " Nice butt, Bruce". She Is referring to actor Bruce Dern and the movie she Is watching Is called "Silent Running".
The trivia items below may give away important plot points.
In the opening scenes where the father is driving on the cliff with the kids, the license plate of their car spells "no 1 dad", a joke by the directors considering he Is In the midst of murdering his family and on his way to kill the children and himself.