Claudius is power-hungry, to the point of it dominating all of his decisions, even at the cost of human lives. It drives him to murder his brother and marry his sister-in-law, it drives him to send dispatches to murder Hamlet, and it plays a role in his manipulation of Laertes at the end, in the duel challenge. His drive for power causes much of the harm done in the play. Laertes has a weakness of vanity; at the beginning of the play we see him departing to seek fortune, experience and a name for himself in the world. It is while he is gone boosting his vanity that his father is killed and Ophelia goes mad; without him there to support either one of them, they fell prey to the events at the castle. Vanity also prompts Laertes to revenge at the end--he has to maintain an image of the protecting son avenging his father's name. His vanity leaves him vulnerable to manipulation and schemes.
I feel that Ophelia's main weakness is her lack of a backbone, or confidence and individuality. She allows herself to be a pawn in the hands of her father and the king and queen. Even though she loved Hamlet and had a relationship with him, she doesn't hesitate to break it off with him and return his things, all so that meddling people can observe Hamlet's behavior. She does whatever her father tells her to do, and doesn't voice her own opinion or desires. Maybe she doesn't have her own opinions, which leads to her malleability. Ophelia is weak, and lacks the courage to voice her own will; this leads to her shunning of Hamlet and her inability to cope when the person who guided her life, her father, died.
And then there's Hamlet. Thousands of essays have been written about what his potentially most fatal weakness could have been. I think it was his lack of action--his indecisiveness, that lead to all of the tragedy in the play. Hamlet's indecisiveness makes Claudius suspicious and gives him time to hatch evil plans against Hamlet. Hamlet's lack of quick, decisive action allows all of the events of the play to happen in their own time, leading to everyone's deaths. I also provided a link below that discusses other potential weaknesses of Hamlet.
I hope that helped; good luck!