Language
The heptapod language is a set of uniquely intricate symbols that hold within them a non-linear context that is outside of our current linguistic structure. This is a symbol for how language has the ability to hold within it great power and meaning if spoken and interpreted correctly.
Abbott and Costello
Donelly gives the heptapods the nicknames Abbott and Costello after the famous comedy duo. This is a symbol of his affinity towards them rather than assuming they are creatures intending to kill.
Shadow
Louise is seen only in shadow with a shot facing out towards the water view from the inside of her home. This is a symbol that Louise's life has become burdened with great grief and darkness as she has had to choose life or death for her daughter even before she was born, and once she was welcomed into this life Louise would know that she will not be in it for very long. The image represents that weight.
Bomb
Rogue soldiers plant a bomb in the heptapod ship that has landed in Montana. This is a symbol of how many people choose to act out of fear and self-preservation without the proper intelligence necessary to determine if what they believe is a threat is actually one or not.
Opening Scene
The opening scene reveals that Louise's daughter has died of an unknown illness. This is a symbol of the great weight of loss of love that Louise must carry throughout the film as she makes every decision.
The bird in a cage
When traveling inside the Shell, the team takes with them a bird locked in a rectangular cage, the presence of which is never explained. This is a symbol for how the heptapods viewed humans, with the bird representing the human race while the cage is the way humans think about time.