In Shakespeare's play Julius Caesar, how is Brutus' greatness also his weakness?

What distinguishes Brutus from the others is that he acts on noble intentions, but these also make him naïve. 

Unlike many of the other conspirators, Brutus has no ambition in the purest sense.  He involves himself in the conspiracy because he believes it is for the good of Rome.  As long as Caesar is in power, by Brutus’s thinking, Rome cannot remain a republic.  Caesar will make himself king. 

Brutus does not desire to be king.  He wants things to go back to the way they were in what he sees as the golden days of Rome.  He pictures an idealized Rome, where the senate and republic reign supreme.  To this end, he is willing to assassinate Caesar. 

When Brutus decides that Caesar has to die, he convinces himself with a flowery speech about Caesar’s death. 

It must be by his death: and for my part,
I know no personal cause to spurn at him,
But for the general. He would be crown'd:
How that might change his nature, there's the question.
It is the bright day that brings forth the adder;
And that craves wary walking. (Act 2, Scene 1) 

While it may be noble to want to kill Caesar only for the good of his country, Brutus’s desire to make the assassination honorable causes trouble for his group.  Noble and practical are not the same thing.  Brutus refuses to kill anyone other than Caesar, leaving Mark Antony free to wreak havoc.  He also insists that the killing be public in the capital at the senate meeting, which makes it more dangerous.  The group has to get Caesar to that spot on that day, and prevent anyone from interrupting them. 

Brutus even allows Mark Antony to speak after him at Caesar’s funeral.  This may be noble, but it is a huge mistake.  Antony turns the people against Brutus and the others, and they have to go on the run and on the offensive. 

After his death, Antony acknowledges that Brutus may have had good intentions. 

This was the noblest Roman of them all:
All the conspirators save only he
Did that they did in envy of great Caesar;
He only, in a general honest thought
And common good to all, made one of them.
His life was gentle, and the elements
So mix'd in him that Nature might stand up
And say to all the world 'This was a man!' (Act 5, Scene 5) 

Thus, Brutus’s greatest strength was also his greatest weakness.  He truly loved Rome, and he was not an ambitious person.  However, he also felt that he could control the forces that he was trying to direct, and make sure that everything fit his idealistic version of tyranticide.  He was in over his head, and continually failed to acknowledge how things were really going.