What are some tragic flaws of Julius Caesar and how do his tragic flaws lead to his down fall in Julius Caesar by Shakespeare?

Julius Caesar is arrogant, power-hungry, and ambitious.

At the beginning of Shakespeare's drama, in anticipation of the return of Julius Caesar to Rome, Flavius and Marullus, two tribunes who are opposed to Caesar's growing power, chastise the citizens who are excited about Caesar's victorious return. The tribunes remind these citizens of the beloved Pompey, who was part of the triumvirate with Caesar, but has been killed in the civil war with Caesar:

And do you now put on your best attire?....
And do you now strew flowers in his way
That comes in triumph over Pompey's blood? (1.1.50-54)

So, now only Caesar is left, and Flavius and Marullus are concerned that the Roman Republic, which was designed to be anti-monarchy, may soon change.

After Caesar arrives, the crowds cheer him and he revels in the adulation. When the soothsayer tells him to beware of the Ides of March, Caesar calls him a dreamer, and arrogantly dismisses him. His inflated opinion of himself later leads Caesar to also dismiss his wife's fears before he goes to the Senate on the Ides of March. This action, of course, directly leads to his downfall. 

In addition to his inflated ego, Caesar appears eager for power as described by Casca, who reports to Brutus how Marc Antony offered Caesar a coronet three times, and although Caesar refused it each time, he seemed loathe to do so. Such a report, as well as the observations of Brutus regarding Caesar's victory over Pompey, who was once his friend and ally, cause Brutus much consternation. He worries that Caesar will "disjoin [separate]/ Remorse from power"(2.1.19) and become tyrannical if he is granted the power and authority of kingship. It is, indeed, this concern of Brutus about Caesar's arrogance and lust for power that leads him to join in the conspiracy to assassinate Caesar. With the influential Brutus on their side, the conspirators then slay Caesar.