Marriage Ring
The marriage rings that Nicole and Charlie have are initially symbolic of, as most rings are, their deep and abiding love for each other. As the story progresses, and as Charlie and Nicole's marriage unravels and ultimately ends, their marriage rings come to represent the best and the link that they still share: their son, Henry.
Lawyers
The lawyers that Charlie and Nicole retain and use are symbolic of the business transaction that marriage and love becomes after divorce proceedings are initiated.
Charlie's Fellowship Grant
Charlie's fellowship grant is symbolic of the success he had sought for all of his life and an acknowledgment of his intelligence and genius, something that he has sought for much of his life. Charlie's quest for success is one of the contributing factors to his breakup with Nicole.
Charlie's New York Residence
Charlie's New York Residence is symbolic of his obstinance and his unwillingness to make tough choices that would benefit him and his family. Ultimately, Charlie's unwillingness to do what is best for his family is one of the primary reasons behind his divorce with Nicole. He wants career success more than anything in the world and is willing to forgo his family for a chance at success.
Charlie's Obstinance
Charlie's obstinance is a common motif in the film. Throughout the film, Charlie is unwilling to compromise with Nicole, unwilling to work with his lawyer, unwilling to move to Los Angeles despite his ex-wife and son moving there and despite the tremendous opportunity for him there, and is unwilling to change how he acts with his son.