BB bullet (Symbol)
Early on in the film, we see Royal playing with Chas and Richie as children. They are engaged in a fight with BB guns, and from the roof of a summer home, Royal shoots Chas in the hand with the gun, in spite of their being on the same team. The bullet remains lodged in Chas' knuckle well into adulthood, and serves as a symbol of his father's neglect and betrayal. In order to access the resentment and distrust he feels towards his absentee father, Chas need look no further than the outline of the BB bullet in his knuckle to remember what a traitorous and no-good man Royal really is.
Margot's wooden finger (symbol)
Margot, like Chas with his BB bullet, also has an unusual hand. On one hand, a finger is missing, the product of a wood chopping error on the part of her biological father in Indiana. She now has a wooden finger in its place, which symbolizes her difference from the rest of her adopted family. The missing finger represents the ways that her biological father hurt her accidentally when she went to make a connection with him, and that she will never quite belong in any family of which she is a part. Margot's wooden finger sets her apart, alienating her, but also making her unique.
Royal's Indulgences (Motif)
Throughout, Royal is shown to be an indulgent man who likes to enjoy the pleasures and vices of life. He drinks martinis and other drinks throughout, eats hamburgers almost constantly, smokes, and lives life on the edge. At the beginning of the film, these vices represent Royal's selfishness and his outsized focus on his baser desires. In the middle of the film, when he is living at the Tenenbaum residence, they represent his deception; no one with a terminal stomach cancer diagnosis could be living, eating, smoking, and drinking as recklessly as Royal. By the end, his vices represent his ability to enjoy life, to live it to the fullest, and although his vices ultimately kill him—he suffers a fatal heart attack while recklessly riding on the back of a garbage truck with Chas, Ari, and Uzi—no one can say that Royal didn't know how to relax and enjoy life while he lived it.
Mordecai (Motif)
Richie is an eccentric child, who raises hawks in a small structure on top of the Tenenbaum residence. When he returns home from the cruise, we see him letting Mordecai fly free, which represents the ways that he himself is growing up, becoming an adult, and trying to ignore and repress his love for his adopted sister, Margot. Immediately after setting Mordecai free, Richie reads a book of Margot's plays. Later, when he and Royal talk about his love for Margot on the roof of the hotel where Royal works, Mordecai finds Richie. Royal points out how miraculous it is that the hawk found its owner, as if it had radar. Mordecai coming back symbolizes the fact that Richie is coming to terms with and dealing with his love for his sister, Margot, and bringing that information to a trusted confidante, his father.
Dalmatians (Motif)
When we first meet Chas as a child, he is a business and science prodigy, in that he has bred Dalmatian mice with spots, which he sells to pet stores in Little Tokyo. The Dalmatian mice represent Chas' childhood success, a success for which, he feels, his father never gave him credit. When Eli Cash mows down Ari and Uzi's trusted beagle, Buckley, Royal goes to the firemen who come to the scene, and buys a Dalmatian that he gives to Chas and the boys as a way of replacing Buckley. The recurrence of the Dalmatian animal represents the fact that Royal is seeing Chas for his accomplishments and trying to be more of a part of his life.
