Todd's desk set (Symbol)
The desk set that Todd's parents send him on his birthday, identical to the one he received last year, is a symbol of their distance from him, a demonstration that they act on autopilot when trying to show him love. His decision at Neil's encouragement to throw it over the edge of the building symbolizes his resentment toward them.
Tearing out the textbook intros (Symbol)
Keating's request that his students tear out the introduction of their textbook is symbolic of his distaste for the past ways that Welton has taught poetry, and of his desire to be bold, rebellious, and unpredictable, and to encourage his students to be so as well.
Charlie's red lightning bolt (Symbol)
Just before Neil's play, Charlie reveals he's painted a red lightning bolt on his chest, which he claims is a symbol for virility. More broadly, it represents his brash and rebellious nature, one that Mr. Keating helped to stoke.
Mr. Keating is almost never alone (Motif)
There are only two points in the film where Mr. Keating is shown on his own: when he cries in his classroom after Neil's death, and when he waves to Mr. McAllister from his office window after he's been fired. At all other times, he is featured only in scenes with other characters; that is, the writer and director chose to feature Mr. Keating primarily in relation to other people, a motif that reflects his influential nature and that the film isn't so much about him personally, but about the effect he has on others.
Tchaikovsky's 1812 Overture (Motif)
Mr. Keating is frequently heard whistling the introduction from Tchaikovsky's "1812 Overture." The piece is a celebratory commemoration of Russia's defeat of Napoleon, a very positive and uplifting work to accompany a positive and uplifting man.
