In Shakespeare's Macbeth, the tragic figure, Macbeth, is considered to have one tragic flaw, ambition. And one tragic flaw is the norm for a tragedy. One wouldn't expect more than one tragic flaw.
The witches predict that Macbeth will be king, but he is so ambitious that he takes that idea and turns it into I will be king now! And the only way he can make that happen is by assassinating Duncan.
Then, once Duncan is dead and Macbeth is king, that's no longer enough. At that point, being king himself is not good enough--he wants his heirs to be kings as well. He wants to create a dynasty. This leads to the rest of the killings, which cast suspicion upon him.
His ambition leads to the destruction of Duncan, Banquo, and Macduff's family, and ultimately to his own destruction.
Just as a sidenote, if you need a couple of major mistakes Macbeth makes in order to come up with three parts for your answer, you could use Macbeth's killing of the grooms, which was not part of the plan. This raises suspicion, at least in Macduff's mind, that Macbeth is guilty of treachery. A second mistake that he makes occurs when he shuts Lady Macbeth out of the decision-making process: she is the planner of the family. When he starts making decisions for himself, he really starts making mistakes (the rest of the killings, and the failure to kill Fleance).